TSTP Solution File: SCT171+5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SCT171+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 21:48:10 EDT 2022
% Result : Theorem 117.24s 117.43s
% Output : CNFRefutation 135.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 257
% Syntax : Number of formulae : 2687 (1278 unt; 88 typ; 0 def)
% Number of atoms : 28661 (11158 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 581687 (11196 ~;14163 |; 270 &;555855 @)
% ( 35 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 165 ( 165 >; 0 *; 0 +; 0 <<)
% Number of symbols : 91 ( 88 usr; 27 con; 0-6 aty)
% Number of variables : 10290 ( 0 ^10289 !; 1 ?;10290 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_arrow_1212486748le_alt,type,
arrow_1212486748le_alt: $i ).
thf(tp_arrow_1384031255e_indi,type,
arrow_1384031255e_indi: $i ).
thf(tp_arrow_1726925404_above,type,
arrow_1726925404_above: $i ).
thf(tp_arrow_1834574746e_Prof,type,
arrow_1834574746e_Prof: $i ).
thf(tp_arrow_1932713123nimity,type,
arrow_1932713123nimity: $i ).
thf(tp_arrow_1990387629ctator,type,
arrow_1990387629ctator: $i ).
thf(tp_arrow_612047104le_IIA,type,
arrow_612047104le_IIA: $i ).
thf(tp_arrow_638930832le_Lin,type,
arrow_638930832le_Lin: $i ).
thf(tp_arrow_844286440_mkbot,type,
arrow_844286440_mkbot: $i ).
thf(tp_arrow_992993526_mktop,type,
arrow_992993526_mktop: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bool,type,
bool: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_collect,type,
collect: $i > $i ).
thf(tp_combb,type,
combb: $i > $i > $i > $i ).
thf(tp_combc,type,
combc: $i > $i > $i > $i ).
thf(tp_combi,type,
combi: $i > $i ).
thf(tp_combk,type,
combk: $i > $i > $i ).
thf(tp_combs,type,
combs: $i > $i > $i > $i ).
thf(tp_d,type,
d: $i ).
thf(tp_e,type,
e: $i ).
thf(tp_f,type,
f: $i ).
thf(tp_fFalse,type,
fFalse: $i ).
thf(tp_fTrue,type,
fTrue: $i ).
thf(tp_fequal,type,
fequal: $i > $i ).
thf(tp_finite_card,type,
finite_card: $i > $i ).
thf(tp_fun,type,
fun: $i > $i > $i ).
thf(tp_h,type,
h: $i ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_hilbert_inv_into,type,
hilbert_inv_into: $i > $i > $i ).
thf(tp_if,type,
if: $i > $i ).
thf(tp_inj_on,type,
inj_on: $i > $i > $i ).
thf(tp_lab,type,
lab: $i ).
thf(tp_lba,type,
lba: $i ).
thf(tp_linorder,type,
linorder: $i > $o ).
thf(tp_member,type,
member: $i > $i ).
thf(tp_n,type,
n: $i ).
thf(tp_nat,type,
nat: $i ).
thf(tp_ord,type,
ord: $i > $o ).
thf(tp_ord_less,type,
ord_less: $i > $i ).
thf(tp_order,type,
order: $i > $o ).
thf(tp_p,type,
p: $i ).
thf(tp_pi,type,
pi: $i > $i > $i ).
thf(tp_preorder,type,
preorder: $i > $o ).
thf(tp_product_Pair,type,
product_Pair: $i > $i > $i ).
thf(tp_product_prod,type,
product_prod: $i > $i > $i ).
thf(tp_product_prod_rec,type,
product_prod_rec: $i > $i > $i > $i ).
thf(tp_sK10_X_1,type,
sK10_X_1: $i > $i > $i > $i > $i ).
thf(tp_sK11_SY1310,type,
sK11_SY1310: $i > $i > $i > $i > $i ).
thf(tp_sK12_X_1,type,
sK12_X_1: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY1311,type,
sK13_SY1311: $i > $i > $i > $i > $i ).
thf(tp_sK14_I,type,
sK14_I: $i > $i > $i > $i > $i ).
thf(tp_sK15_X_1,type,
sK15_X_1: $i > $i ).
thf(tp_sK16_SY1312,type,
sK16_SY1312: $i > $i ).
thf(tp_sK17_SY1315,type,
sK17_SY1315: $i > $i ).
thf(tp_sK18_I,type,
sK18_I: $i > $i > $i > $i > $i > $i ).
thf(tp_sK19_I,type,
sK19_I: $i > $i > $i > $i > $i > $i ).
thf(tp_sK1_X_1,type,
sK1_X_1: $i > $i > $i ).
thf(tp_sK20_X_1,type,
sK20_X_1: $i > $i ).
thf(tp_sK21_SY1318,type,
sK21_SY1318: $i > $i ).
thf(tp_sK22_SY1323,type,
sK22_SY1323: $i > $i ).
thf(tp_sK23_SY1327,type,
sK23_SY1327: $i > $i ).
thf(tp_sK24_A_2,type,
sK24_A_2: $i > $i > $i > $i ).
thf(tp_sK25_SY1332,type,
sK25_SY1332: $i > $i > $i > $i ).
thf(tp_sK26_X1,type,
sK26_X1: $i > $i > $i > $i ).
thf(tp_sK27_I,type,
sK27_I: $i > $i > $i > $i > $i ).
thf(tp_sK28_I,type,
sK28_I: $i > $i > $i > $i > $i ).
thf(tp_sK29_I,type,
sK29_I: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK2_X_1,type,
sK2_X_1: $i > $i > $i ).
thf(tp_sK30_I,type,
sK30_I: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK31_I,type,
sK31_I: $i > $i > $i > $i > $i > $i ).
thf(tp_sK32_I,type,
sK32_I: $i > $i > $i > $i > $i > $i ).
thf(tp_sK33_I,type,
sK33_I: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK34_I,type,
sK34_I: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK35_I,type,
sK35_I: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK3_X_1,type,
sK3_X_1: $i > $i > $i ).
thf(tp_sK4_SY1306,type,
sK4_SY1306: $i > $i > $i ).
thf(tp_sK5_SY1308,type,
sK5_SY1308: $i > $i > $i ).
thf(tp_sK6_X_1,type,
sK6_X_1: $i > $i > $i > $i > $i ).
thf(tp_sK7_X_1,type,
sK7_X_1: $i > $i > $i > $i ).
thf(tp_sK8_SY1309,type,
sK8_SY1309: $i > $i > $i > $i ).
thf(tp_sK9_X_1,type,
sK9_X_1: $i > $i > $i > $i > $i ).
thf(tp_ti,type,
ti: $i > $i > $i ).
thf(tp_top,type,
top: $i > $o ).
thf(tp_top_top,type,
top_top: $i > $i ).
thf(tp_undefined,type,
undefined: $i > $i ).
thf(1,axiom,
! [X_a: $i,X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(2,axiom,
! [X_a: $i,X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(3,axiom,
! [P: $i] :
( ( ( ti @ bool @ P )
= fTrue )
| ( ( ti @ bool @ P )
= fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(4,axiom,
hBOOL @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(5,axiom,
! [X_a: $i,X_c: $i,X_b: $i,P: $i,Q: $i,R: $i] :
( ( hAPP @ X_a @ X_c @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) @ ( combs @ X_a @ X_b @ X_c ) @ P ) @ Q ) @ R )
= ( hAPP @ X_b @ X_c @ ( hAPP @ X_a @ ( fun @ X_b @ X_c ) @ P @ R ) @ ( hAPP @ X_a @ X_b @ Q @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(6,axiom,
! [X_b: $i,X_a: $i,P: $i,Q: $i] :
( ( hAPP @ X_b @ X_a @ ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( combk @ X_a @ X_b ) @ P ) @ Q )
= ( ti @ X_a @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(7,axiom,
! [X_a: $i,P: $i] :
( ( hAPP @ X_a @ X_a @ ( combi @ X_a ) @ P )
= ( ti @ X_a @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(8,axiom,
! [X_a: $i,X_c: $i,X_b: $i,P: $i,Q: $i,R: $i] :
( ( hAPP @ X_a @ X_c @ ( hAPP @ X_b @ ( fun @ X_a @ X_c ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ X_b @ ( fun @ X_a @ X_c ) ) @ ( combc @ X_a @ X_b @ X_c ) @ P ) @ Q ) @ R )
= ( hAPP @ X_b @ X_c @ ( hAPP @ X_a @ ( fun @ X_b @ X_c ) @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(9,axiom,
! [X_a: $i,X_c: $i,X_b: $i,P: $i,Q: $i,R: $i] :
( ( hAPP @ X_a @ X_c @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) @ ( hAPP @ ( fun @ X_b @ X_c ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) @ ( combb @ X_b @ X_c @ X_a ) @ P ) @ Q ) @ R )
= ( hAPP @ X_b @ X_c @ P @ ( hAPP @ X_a @ X_b @ Q @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(10,axiom,
! [P: $i] :
( ( ( ti @ bool @ P )
= fTrue )
| ( ( ti @ bool @ P )
= fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(11,axiom,
! [X_a: $i,X: $i,Y: $i] :
( ( hAPP @ X_a @ X_a @ ( hAPP @ X_a @ ( fun @ X_a @ X_a ) @ ( hAPP @ bool @ ( fun @ X_a @ ( fun @ X_a @ X_a ) ) @ ( if @ X_a ) @ fFalse ) @ X ) @ Y )
= ( ti @ X_a @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(12,axiom,
! [X_a: $i,X: $i,Y: $i] :
( ( hAPP @ X_a @ X_a @ ( hAPP @ X_a @ ( fun @ X_a @ X_a ) @ ( hAPP @ bool @ ( fun @ X_a @ ( fun @ X_a @ X_a ) ) @ ( if @ X_a ) @ fTrue ) @ X ) @ Y )
= ( ti @ X_a @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(13,axiom,
! [T: $i,A: $i] :
( ( ti @ T @ ( ti @ T @ A ) )
= ( ti @ T @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(14,axiom,
ord @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(15,axiom,
top @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(16,axiom,
order @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(17,axiom,
preorder @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(18,axiom,
ord @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(19,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(20,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(21,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(22,axiom,
! [T_2: $i,T_1: $i] :
( ( ord @ T_1 )
=> ( ord @ ( fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(23,axiom,
! [T_2: $i,T_1: $i] :
( ( top @ T_1 )
=> ( top @ ( fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(24,axiom,
! [T_2: $i,T_1: $i] :
( ( order @ T_1 )
=> ( order @ ( fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(25,axiom,
! [T_2: $i,T_1: $i] :
( ( preorder @ T_1 )
=> ( preorder @ ( fun @ T_2 @ T_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(26,axiom,
~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(27,axiom,
~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ a ) @ b ) ) @ lba ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(28,axiom,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ a ) @ b ) ) @ lab ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(29,axiom,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(30,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95__096a_A_126_061_Ab_096) ).
thf(31,axiom,
! [I: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
=> ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).
thf(32,axiom,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).
thf(33,axiom,
! [X_a: $i,X_b: $i,A_1: $i] :
( ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ ( hAPP @ ( fun @ X_b @ bool ) @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( combk @ ( fun @ X_b @ bool ) @ X_a ) @ ( top_top @ ( fun @ X_b @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Pi__UNIV) ).
thf(34,axiom,
! [Fa: $i,I_1: $i] :
( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) )
<=> ! [X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
=> ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ I_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_dictator__def) ).
thf(35,axiom,
! [X_a: $i,A_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_a ) @ ( fun @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_a ) ) @ ( combi @ X_a ) ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) ) @ ( pi @ X_a @ X_a ) @ A_1 ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( combk @ ( fun @ X_a @ bool ) @ X_a ) @ A_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_funcset__id) ).
thf(36,axiom,
! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ ( hAPP @ ( fun @ X_b @ bool ) @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( combk @ ( fun @ X_b @ bool ) @ X_a ) @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_funcset__mem) ).
thf(37,axiom,
( arrow_1834574746e_Prof
= ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ arrow_1384031255e_indi ) @ arrow_638930832le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Prof__def) ).
thf(38,axiom,
! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ B @ X_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Pi__mem) ).
thf(39,axiom,
! [Na: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ Na ) ) ) @ lab ) ) @ lba ) ) @ arrow_1834574746e_Prof ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_PiProf) ).
thf(40,axiom,
! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ? [X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ X_1 ) @ arrow_638930832le_Lin ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_complete__Lin) ).
thf(41,axiom,
! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ B @ X_2 ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_PiE) ).
thf(42,axiom,
! [I_1: $i,Fa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Fa ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
=> ( ! [X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
=> ! [A_2: $i,B_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ A_2 )
!= ( ti @ arrow_1212486748le_alt @ B_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ I_1 ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_dictatorI) ).
thf(43,axiom,
! [X_2: $i,Y_1: $i,L: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
<=> ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
& ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) ) )
& ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) ) ) )
& ( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_in__above) ).
thf(44,axiom,
! [L: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ arrow_1384031255e_indi ) @ L ) ) @ arrow_1834574746e_Prof ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_const__Lin__Prof) ).
thf(45,axiom,
! [L: $i,X_2: $i,Y_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ X_2 ) @ Y_1 ) ) @ arrow_638930832le_Lin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_above__Lin) ).
thf(46,axiom,
! [X_2: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ X_2 ) ) @ arrow_638930832le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_mkbot__Lin) ).
thf(47,axiom,
! [X_2: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ X_2 ) ) @ arrow_638930832le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mktop__Lin) ).
thf(48,axiom,
! [X_a: $i,Pa: $i] :
( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ Pa )
= ( ti @ ( fun @ X_a @ bool ) @ Pa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(49,axiom,
! [X_a: $i,X_2: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
<=> ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(50,axiom,
! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ! [X_1: $i] :
( ( hAPP @ X_a @ X_b @ F @ X_1 )
= ( hAPP @ X_a @ X_b @ G @ X_1 ) )
=> ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(51,axiom,
! [X_2: $i,Y_1: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Y_1 ) @ X_2 ) ) @ L ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_notin__Lin__iff) ).
thf(52,axiom,
! [Aa: $i,Ba: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ L ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ L ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Lin__irrefl) ).
thf(53,axiom,
hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ lab ) @ arrow_638930832le_Lin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72__096Lab_A_058_ALin_096) ).
thf(54,axiom,
hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ lba ) @ arrow_638930832le_Lin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71__096Lba_A_058_ALin_096) ).
thf(55,axiom,
hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ f ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_assms_I1_J) ).
thf(56,axiom,
! [X_a: $i,X_b: $i,F: $i] :
( ! [X_1: $i,Y_2: $i] :
( ( ( hAPP @ X_a @ X_b @ F @ X_1 )
= ( hAPP @ X_a @ X_b @ F @ Y_2 ) )
=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Y_2 ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_injI) ).
thf(57,axiom,
! [X_a: $i,X_b: $i,G: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
=> ( ! [X_1: $i] :
( ( hAPP @ X_a @ X_b @ F @ ( hAPP @ X_b @ X_a @ G @ X_1 ) )
= ( ti @ X_b @ X_1 ) )
=> ( ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F )
= ( ti @ ( fun @ X_b @ X_a ) @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_inj__imp__inv__eq) ).
thf(58,axiom,
! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
=> ( ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
=> ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_injD) ).
thf(59,axiom,
! [X_a: $i,A_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_a ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_a ) @ ( combi @ X_a ) ) @ A_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_inj__on__id2) ).
thf(60,axiom,
! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
=> ( ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
=> ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_inj__onD) ).
thf(61,axiom,
! [X_a: $i,X_b: $i,Y_1: $i,X_2: $i,F: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
=> ( ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_inj__on__iff) ).
thf(62,axiom,
! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
=> ( ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
=> ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_inj__on__contraD) ).
thf(63,axiom,
! [X_a: $i,X_b: $i,F: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
<=> ! [X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
=> ! [Xa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Xa ) @ A_1 ) )
=> ( ( ( hAPP @ X_a @ X_b @ F @ X_1 )
= ( hAPP @ X_a @ X_b @ F @ Xa ) )
=> ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Xa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_inj__on__def) ).
thf(64,axiom,
! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
=> ( ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_inj__eq) ).
thf(65,axiom,
! [X_a: $i,X_b: $i,Y_1: $i,X_2: $i,F: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
=> ( ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( ti @ X_b @ Y_1 ) )
=> ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ A_1 ) @ F ) @ Y_1 )
= ( ti @ X_a @ X_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_inv__into__f__eq) ).
thf(66,axiom,
! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
=> ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ A_1 ) @ F ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) )
= ( ti @ X_a @ X_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_inv__into__f__f) ).
thf(67,axiom,
! [X_c: $i,X_a: $i,X_b: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ ( fun @ X_c @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ X_b ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) ) @ ( combb @ X_b @ ( fun @ X_c @ X_b ) @ X_a ) @ ( combk @ X_b @ X_c ) ) @ F ) ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_inj__fun) ).
thf(68,axiom,
! [X_a: $i,X_b: $i,X_2: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
=> ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) )
= ( ti @ X_a @ X_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_inv__f__f) ).
thf(69,axiom,
! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
=> ( ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( ti @ X_b @ Y_1 ) )
=> ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F ) @ Y_1 )
= ( ti @ X_a @ X_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_inv__f__eq) ).
thf(70,axiom,
! [X_a: $i] :
( ( top @ X_a )
=> ! [Aa: $i] :
( ( ( ti @ X_a @ Aa )
!= ( top_top @ X_a ) )
<=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Aa ) @ ( top_top @ X_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__top) ).
thf(71,axiom,
! [X_a: $i,X_b: $i,S: $i,R_1: $i] :
( ! [X_1: $i,Xa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ R_1 ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ S ) ) )
<=> ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_pred__equals__eq2) ).
thf(72,axiom,
! [X_a: $i] :
( ( top_top @ ( fun @ X_a @ bool ) )
= ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ ( hAPP @ bool @ ( fun @ X_a @ bool ) @ ( combk @ bool @ X_a ) @ fTrue ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_UNIV__def) ).
thf(73,axiom,
! [X_a: $i] :
( ( preorder @ X_a )
=> ! [X: $i] :
~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order__less__irrefl) ).
thf(74,axiom,
! [X_a: $i] :
( ( linorder @ X_a )
=> ! [X_2: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
<=> ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_linorder__neq__iff) ).
thf(75,axiom,
! [X_a: $i] :
( ( linorder @ X_a )
=> ! [X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
<=> ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_not__less__iff__gr__or__eq) ).
thf(76,axiom,
! [X_a: $i] :
( ( linorder @ X_a )
=> ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_linorder__less__linear) ).
thf(77,axiom,
! [X_a: $i] :
( ( linorder @ X_a )
=> ! [Y_1: $i,X_2: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
=> ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_linorder__antisym__conv3) ).
thf(78,axiom,
! [X_a: $i] :
( ( linorder @ X_a )
=> ! [X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
=> ( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_linorder__neqE) ).
thf(79,axiom,
! [X_a: $i] :
( ( order @ X_a )
=> ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ( X != Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__imp__neq) ).
thf(80,axiom,
! [X_a: $i] :
( ( preorder @ X_a )
=> ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_order__less__not__sym) ).
thf(81,axiom,
! [X_a: $i] :
( ( preorder @ X_a )
=> ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_order__less__imp__not__less) ).
thf(82,axiom,
! [X_a: $i] :
( ( order @ X_a )
=> ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ( X != Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_order__less__imp__not__eq) ).
thf(83,axiom,
! [X_a: $i] :
( ( order @ X_a )
=> ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ( Y != X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_order__less__imp__not__eq2) ).
thf(84,axiom,
! [X_a: $i] :
( ( preorder @ X_a )
=> ! [Pa: $i,X_2: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
=> ( hBOOL @ Pa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_order__less__imp__triv) ).
thf(85,axiom,
! [X_a: $i] :
( ( preorder @ X_a )
=> ! [A_3: $i,B_2: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) )
=> ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_order__less__asym_H) ).
thf(86,axiom,
! [X_a: $i] :
( ( order @ X_a )
=> ! [B_2: $i,A_3: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) )
=> ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_xt1_I9_J) ).
thf(87,axiom,
! [X_a: $i] :
( ( ord @ X_a )
=> ! [C: $i,A_3: $i,B_2: $i] :
( ( A_3 = B_2 )
=> ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ C ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_ord__eq__less__trans) ).
thf(88,axiom,
! [X_a: $i] :
( ( order @ X_a )
=> ! [C: $i,A_3: $i,B_2: $i] :
( ( A_3 = B_2 )
=> ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ B_2 ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ A_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_xt1_I1_J) ).
thf(89,axiom,
! [X_a: $i] :
( ( ord @ X_a )
=> ! [C: $i,A_3: $i,B_2: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) )
=> ( ( B_2 = C )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_ord__less__eq__trans) ).
thf(90,axiom,
! [X_a: $i] :
( ( order @ X_a )
=> ! [C: $i,B_2: $i,A_3: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) )
=> ( ( B_2 = C )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ A_3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_xt1_I2_J) ).
thf(91,axiom,
! [X_a: $i] :
( ( preorder @ X_a )
=> ! [Z: $i,X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ Z ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Z ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_order__less__trans) ).
thf(92,axiom,
! [X_a: $i] :
( ( order @ X_a )
=> ! [Z: $i,Y: $i,X: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) )
=> ( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Z ) @ Y ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Z ) @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_xt1_I10_J) ).
thf(93,axiom,
! [X_a: $i] :
( ( preorder @ X_a )
=> ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_order__less__asym) ).
thf(94,axiom,
! [X_a: $i] :
( ( linorder @ X_a )
=> ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
=> ( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
=> ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_linorder__cases) ).
thf(95,axiom,
! [X_a: $i] :
( ( top @ X_a )
=> ! [A_3: $i] :
~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ ( top_top @ X_a ) ) @ A_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_not__top__less) ).
thf(96,axiom,
! [X_b: $i,X_a: $i] :
( ( top @ X_a )
=> ! [X_2: $i] :
( ( hAPP @ X_b @ X_a @ ( top_top @ ( fun @ X_b @ X_a ) ) @ X_2 )
= ( top_top @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_top__apply) ).
thf(97,axiom,
! [X_b: $i,X_c: $i,X_a: $i,F1: $i,Aa: $i,Ba: $i] :
( ( hAPP @ ( product_prod @ X_b @ X_c ) @ X_a @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ X_a ) ) @ ( fun @ ( product_prod @ X_b @ X_c ) @ X_a ) @ ( product_prod_rec @ X_b @ X_c @ X_a ) @ F1 ) @ ( hAPP @ X_c @ ( product_prod @ X_b @ X_c ) @ ( hAPP @ X_b @ ( fun @ X_c @ ( product_prod @ X_b @ X_c ) ) @ ( product_Pair @ X_b @ X_c ) @ Aa ) @ Ba ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ Aa ) @ Ba ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_prod_Orecs) ).
thf(98,axiom,
! [X_a: $i,X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_iso__tuple__UNIV__I) ).
thf(99,axiom,
! [X_a: $i,X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_UNIV__I) ).
thf(100,axiom,
! [X_a: $i,X_2: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( top_top @ ( fun @ X_a @ bool ) ) @ X_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top1I) ).
thf(101,axiom,
! [Fa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ Fa ) )
<=> ! [X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
=> ! [A_2: $i,B_1: $i] :
( ! [I: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ I ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_unanimity__def) ).
thf(102,axiom,
! [Fa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ Fa ) )
<=> ! [X_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
=> ! [Xa: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Xa ) @ arrow_1834574746e_Prof ) )
=> ! [A_2: $i,B_1: $i] :
( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ I ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ I ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ Xa ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IIA__def) ).
thf(103,axiom,
! [X_b: $i,X_a: $i,Aa: $i,Ba: $i,A_4: $i,B_3: $i] :
( ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ Aa ) @ Ba )
= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_4 ) @ B_3 ) )
<=> ( ( ( ti @ X_a @ Aa )
= ( ti @ X_a @ A_4 ) )
& ( ( ti @ X_b @ Ba )
= ( ti @ X_b @ B_3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Pair__eq) ).
thf(104,axiom,
! [X_b: $i,X_a: $i,A_3: $i,B_2: $i,A_5: $i,B_4: $i] :
( ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_3 ) @ B_2 )
= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_5 ) @ B_4 ) )
=> ~ ( ( ( ti @ X_a @ A_3 )
= ( ti @ X_a @ A_5 ) )
=> ( ( ti @ X_b @ B_2 )
!= ( ti @ X_b @ B_4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__inject) ).
thf(105,axiom,
hBOOL @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ bool ) @ ( inj_on @ arrow_1384031255e_indi @ nat ) @ h ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injh) ).
thf(106,axiom,
hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ n ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ nat @ ( finite_card @ arrow_1384031255e_indi ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n_I1_J) ).
thf(107,axiom,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(108,axiom,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ e ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(109,axiom,
hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) @ arrow_1834574746e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).
thf(110,axiom,
! [X_a: $i,X_b: $i,Pa: $i] :
( ! [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) )
<=> ! [A_2: $i,B_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_2 ) @ B_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_split__paired__All) ).
thf(111,axiom,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
thf(112,axiom,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(113,axiom,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ ( hAPP @ nat @ arrow_1384031255e_indi @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ nat @ arrow_1384031255e_indi ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ nat @ arrow_1384031255e_indi ) ) @ ( hilbert_inv_into @ arrow_1384031255e_indi @ nat ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ) @ h ) @ n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).
thf(114,axiom,
! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) )
<=> ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
=> ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).
thf(115,axiom,
! [P_1: $i,Pa: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ I ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ I ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C3_C) ).
thf(116,axiom,
! [P_1: $i,Pa: $i,A_4: $i,B_3: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ A_4 )
!= ( ti @ arrow_1212486748le_alt @ B_3 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ I ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ I ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).
thf(117,axiom,
! [P_1: $i,Pa: $i,Ca: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ Ba )
!= ( ti @ arrow_1212486748le_alt @ Ca ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ca ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ I ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ I ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C4_C) ).
thf(118,axiom,
! [P_1: $i,Pa: $i,A_4: $i,B_3: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ A_4 )
!= ( ti @ arrow_1212486748le_alt @ B_3 ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ B_3 ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ Ba )
!= ( ti @ arrow_1212486748le_alt @ A_4 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ I ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ I ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C1_C) ).
thf(119,axiom,
! [P_1: $i,Pa: $i,A_4: $i,B_3: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ A_4 )
!= ( ti @ arrow_1212486748le_alt @ B_3 ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ Aa )
!= ( ti @ arrow_1212486748le_alt @ B_3 ) )
=> ( ( ( ti @ arrow_1212486748le_alt @ Ba )
!= ( ti @ arrow_1212486748le_alt @ A_4 ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
=> ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ I ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ I ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C2_C) ).
thf(120,axiom,
! [X_2: $i,Y_1: $i,L: $i,Z_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) )
<=> ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
& ( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
=> ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__mktop) ).
thf(121,axiom,
! [X_2: $i,Y_1: $i,L: $i,Z_1: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) )
<=> ( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
& ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
=> ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ( ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_in__mkbot) ).
thf(122,axiom,
hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ p ) @ arrow_1834574746e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).
thf(123,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).
thf(124,axiom,
hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).
thf(125,axiom,
hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(126,axiom,
( ( ti @ nat @ n )
= n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_n_____res) ).
thf(127,axiom,
( ( ti @ ( fun @ arrow_1384031255e_indi @ nat ) @ h )
= h ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_h_____res) ).
thf(128,axiom,
( ( ti @ arrow_1212486748le_alt @ e )
= e ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_e_____res) ).
thf(129,axiom,
( ( ti @ arrow_1212486748le_alt @ b )
= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_b_____res) ).
thf(130,axiom,
( ( ti @ arrow_1212486748le_alt @ a )
= a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_a_____res) ).
thf(131,axiom,
( ( ti @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ lba )
= lba ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_Lba_____res) ).
thf(132,axiom,
( ( ti @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ lab )
= lab ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_Lab_____res) ).
thf(133,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) ) @ ( member @ X_a ) )
= ( member @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(134,axiom,
! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] :
( ( ti @ X_c @ ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) )
= ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(135,axiom,
! [X_a: $i,X_c: $i,B_1_1: $i,B_2_1: $i] :
( ( hAPP @ X_a @ X_c @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(136,axiom,
! [X_a: $i,X_c: $i,B_1_1: $i,B_2_1: $i] :
( ( hAPP @ X_a @ X_c @ ( ti @ ( fun @ X_a @ X_c ) @ B_1_1 ) @ B_2_1 )
= ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(137,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
= ( fequal @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(138,axiom,
( ( ti @ bool @ fTrue )
= fTrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
thf(139,axiom,
( ( ti @ bool @ fFalse )
= fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
thf(140,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
= ( collect @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(141,axiom,
! [X_b: $i,X_c: $i,X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_b @ ( fun @ X_c @ X_a ) ) @ ( fun @ ( product_prod @ X_b @ X_c ) @ X_a ) ) @ ( product_prod_rec @ X_b @ X_c @ X_a ) )
= ( product_prod_rec @ X_b @ X_c @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Product__Type_Oprod_Oprod__rec_res) ).
thf(142,axiom,
! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) ) @ ( product_Pair @ X_a @ X_b ) )
= ( product_Pair @ X_a @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Product__Type_OPair_res) ).
thf(143,axiom,
! [X_a: $i] :
( ( top @ X_a )
=> ( ( ti @ X_a @ ( top_top @ X_a ) )
= ( top_top @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Otop__class_Otop_res) ).
thf(144,axiom,
! [X_a: $i] :
( ( ord @ X_a )
=> ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( ord_less @ X_a ) )
= ( ord_less @ X_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).
thf(145,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ bool @ ( fun @ X_a @ ( fun @ X_a @ X_a ) ) ) @ ( if @ X_a ) )
= ( if @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_If_res) ).
thf(146,axiom,
! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) ) @ ( hilbert_inv_into @ X_a @ X_b ) )
= ( hilbert_inv_into @ X_a @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Hilbert__Choice_Oinv__into_res) ).
thf(147,axiom,
! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(148,axiom,
! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) ) @ ( pi @ X_a @ X_b ) )
= ( pi @ X_a @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_FuncSet_OPi_res) ).
thf(149,axiom,
! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) ) @ ( inj_on @ X_a @ X_b ) )
= ( inj_on @ X_a @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Fun_Oinj__on_res) ).
thf(150,axiom,
( ( ti @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ nat ) @ ( finite_card @ arrow_1384031255e_indi ) )
= ( finite_card @ arrow_1384031255e_indi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).
thf(151,axiom,
! [X_a: $i,X_b: $i,X_c: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) ) @ ( combs @ X_a @ X_b @ X_c ) )
= ( combs @ X_a @ X_b @ X_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
thf(152,axiom,
! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( combk @ X_a @ X_b ) )
= ( combk @ X_a @ X_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
thf(153,axiom,
! [X_a: $i] :
( ( ti @ ( fun @ X_a @ X_a ) @ ( combi @ X_a ) )
= ( combi @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
thf(154,axiom,
! [X_a: $i,X_b: $i,X_c: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ X_b @ ( fun @ X_a @ X_c ) ) ) @ ( combc @ X_a @ X_b @ X_c ) )
= ( combc @ X_a @ X_b @ X_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
thf(155,axiom,
! [X_b: $i,X_c: $i,X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_b @ X_c ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) ) @ ( combb @ X_b @ X_c @ X_a ) )
= ( combb @ X_b @ X_c @ X_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
thf(156,axiom,
( ( ti @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ arrow_1932713123nimity )
= arrow_1932713123nimity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Ounanimity_res) ).
thf(157,axiom,
( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_992993526_mktop )
= arrow_992993526_mktop ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omktop_res) ).
thf(158,axiom,
( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_844286440_mkbot )
= arrow_844286440_mkbot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omkbot_res) ).
thf(159,axiom,
( ( ti @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ arrow_1990387629ctator )
= arrow_1990387629ctator ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Odictator_res) ).
thf(160,axiom,
( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ arrow_1726925404_above )
= arrow_1726925404_above ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Oabove_res) ).
thf(161,axiom,
( ( ti @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ arrow_1834574746e_Prof )
= arrow_1834574746e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OProf_res) ).
thf(162,axiom,
( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ arrow_638930832le_Lin )
= arrow_638930832le_Lin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OLin_res) ).
thf(163,axiom,
( ( ti @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ arrow_612047104le_IIA )
= arrow_612047104le_IIA ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OIIA_res) ).
thf(164,axiom,
( ( ti @ arrow_1212486748le_alt @ d )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_d_____res) ).
thf(165,axiom,
( ( ti @ arrow_1212486748le_alt @ c )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_c_____res) ).
thf(166,axiom,
( ( ti @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ p )
= p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_P_____res) ).
thf(167,axiom,
( ( ti @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ f )
= f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_F_res) ).
thf(168,axiom,
! [B_1_1: $i] :
( ( hBOOL @ ( ti @ bool @ B_1_1 ) )
<=> ( hBOOL @ B_1_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(169,conjecture,
hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(170,negated_conjecture,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[169]) ).
thf(171,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[170]) ).
thf(172,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1]) ).
thf(173,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( ord @ T_1 )
| ( ord @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(174,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( top @ T_1 )
| ( top @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(175,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( order @ T_1 )
| ( order @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(176,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( preorder @ T_1 )
| ( preorder @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(177,plain,
( ( ( a != b ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(178,plain,
( ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(179,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(180,plain,
( ( ! [Fa: $i,I_1: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ I_1 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK1_X_1 @ I_1 @ Fa ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ I_1 @ Fa ) @ I_1 ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) ) )
& ! [Fa: $i,I_1: $i] :
( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ I_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(181,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ ( hAPP @ ( fun @ X_b @ bool ) @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( combk @ ( fun @ X_b @ bool ) @ X_a ) @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(182,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ B @ X_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(183,plain,
( ( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ Ba @ Aa ) ) @ arrow_638930832le_Lin ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( sK2_X_1 @ Ba @ Aa ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(184,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ B ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ B @ X_2 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(185,plain,
( ( ! [I_1: $i,Fa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Fa ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ Fa @ I_1 ) ) @ arrow_1834574746e_Prof ) )
& ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ Fa @ I_1 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ Fa @ I_1 ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ Fa @ I_1 ) ) @ ( sK5_SY1308 @ Fa @ I_1 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ Fa @ I_1 ) @ I_1 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ Fa @ I_1 ) ) @ ( sK5_SY1308 @ Fa @ I_1 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK3_X_1 @ Fa @ I_1 ) ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(186,plain,
( ( ! [X_2: $i,Y_1: $i,L: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(187,plain,
( ( ! [L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ arrow_1384031255e_indi ) @ L ) ) @ arrow_1834574746e_Prof ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(188,plain,
( ( ! [L: $i,X_2: $i,Y_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ X_2 ) @ Y_1 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(189,plain,
( ( ! [X_2: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ X_2 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(190,plain,
( ( ! [X_2: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ X_2 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(191,plain,
( ( ! [X_a: $i] :
( ! [X_2: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_2 ) ) )
& ! [X_2: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(192,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ( ( hAPP @ X_a @ X_b @ F @ ( sK6_X_1 @ G @ F @ X_b @ X_a ) )
!= ( hAPP @ X_a @ X_b @ G @ ( sK6_X_1 @ G @ F @ X_b @ X_a ) ) )
| ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(193,plain,
( ( ! [X_2: $i] :
( ! [Y_1: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Y_1 ) @ X_2 ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) )
& ! [Y_1: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Y_1 ) @ X_2 ) ) @ L ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(194,plain,
( ( ! [Aa: $i,Ba: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ L ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(195,plain,
( ( ! [X_a: $i,X_b: $i,F: $i] :
( ( ( ( hAPP @ X_a @ X_b @ F @ ( sK7_X_1 @ F @ X_b @ X_a ) )
= ( hAPP @ X_a @ X_b @ F @ ( sK8_SY1309 @ F @ X_b @ X_a ) ) )
& ( ( ti @ X_a @ ( sK7_X_1 @ F @ X_b @ X_a ) )
!= ( ti @ X_a @ ( sK8_SY1309 @ F @ X_b @ X_a ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(196,plain,
( ( ! [X_a: $i,X_b: $i,G: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ ( hAPP @ X_b @ X_a @ G @ ( sK9_X_1 @ F @ G @ X_b @ X_a ) ) )
!= ( ti @ X_b @ ( sK9_X_1 @ F @ G @ X_b @ X_a ) ) )
| ( ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F )
= ( ti @ ( fun @ X_b @ X_a ) @ G ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(197,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(198,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(199,plain,
( ( ! [X_a: $i,X_b: $i,Y_1: $i,X_2: $i] :
( ! [F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) )
& ! [F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(200,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(201,plain,
( ( ! [X_a: $i,X_b: $i] :
( ! [F: $i,A_1: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ ( sK10_X_1 @ A_1 @ F @ X_b @ X_a ) ) @ A_1 ) )
& ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ ( sK11_SY1310 @ A_1 @ F @ X_b @ X_a ) ) @ A_1 ) )
& ( ( hAPP @ X_a @ X_b @ F @ ( sK10_X_1 @ A_1 @ F @ X_b @ X_a ) )
= ( hAPP @ X_a @ X_b @ F @ ( sK11_SY1310 @ A_1 @ F @ X_b @ X_a ) ) )
& ( ( ti @ X_a @ ( sK10_X_1 @ A_1 @ F @ X_b @ X_a ) )
!= ( ti @ X_a @ ( sK11_SY1310 @ A_1 @ F @ X_b @ X_a ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) ) )
& ! [F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
| ! [Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Xa ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_1 )
!= ( hAPP @ X_a @ X_b @ F @ Xa ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Xa ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(202,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i] :
( ! [Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) )
& ! [Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(203,plain,
( ( ! [X_a: $i,X_b: $i,Y_1: $i,X_2: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( ti @ X_b @ Y_1 ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ A_1 ) @ F ) @ Y_1 )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(204,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ A_1 ) @ F ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(205,plain,
( ( ! [X_c: $i,X_a: $i,X_b: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ ( fun @ X_c @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ X_b ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) ) @ ( combb @ X_b @ ( fun @ X_c @ X_b ) @ X_a ) @ ( combk @ X_b @ X_c ) ) @ F ) ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(206,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(207,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( ti @ X_b @ Y_1 ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F ) @ Y_1 )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(208,plain,
( ( ! [X_a: $i] :
( ~ ( top @ X_a )
| ( ! [Aa: $i] :
( ( ( ti @ X_a @ Aa )
= ( top_top @ X_a ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Aa ) @ ( top_top @ X_a ) ) ) )
& ! [Aa: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Aa ) @ ( top_top @ X_a ) ) )
| ( ( ti @ X_a @ Aa )
!= ( top_top @ X_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(209,plain,
( ( ! [X_a: $i,X_b: $i] :
( ! [S: $i,R_1: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ R_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ S ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ R_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ S ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S ) ) )
& ! [S: $i,R_1: $i] :
( ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
!= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S ) )
| ( ! [X_1: $i,Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ R_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ S ) ) )
& ! [X_1: $i,Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ S ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ R_1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(210,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i] :
~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(211,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ( ! [X_2: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(212,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ( ! [X_2: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(213,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(214,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ( ! [Y_1: $i,X_2: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) ) )
& ! [Y_1: $i,X_2: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(215,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ! [X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(216,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( X != Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(217,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(218,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(219,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( X != Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(220,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( Y != X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(221,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [Pa: $i,X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( hBOOL @ Pa ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(222,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [A_3: $i,B_2: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(223,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [B_2: $i,A_3: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(224,plain,
( ( ! [X_a: $i] :
( ~ ( ord @ X_a )
| ! [C: $i,A_3: $i,B_2: $i] :
( ( A_3 != B_2 )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ C ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(225,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [C: $i,A_3: $i,B_2: $i] :
( ( A_3 != B_2 )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ B_2 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ A_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(226,plain,
( ( ! [X_a: $i] :
( ~ ( ord @ X_a )
| ! [C: $i,A_3: $i,B_2: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) )
| ( B_2 != C )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(227,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [C: $i,B_2: $i,A_3: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) )
| ( B_2 != C )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ A_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(228,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [Z: $i,X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ Z ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(229,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [Z: $i,Y: $i,X: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Z ) @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Z ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(230,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(231,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(232,plain,
( ( ! [X_a: $i] :
( ~ ( top @ X_a )
| ! [A_3: $i] :
~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ ( top_top @ X_a ) ) @ A_3 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(233,plain,
( ( ! [X_b: $i,X_a: $i] :
( ~ ( top @ X_a )
| ! [X_2: $i] :
( ( hAPP @ X_b @ X_a @ ( top_top @ ( fun @ X_b @ X_a ) ) @ X_2 )
= ( top_top @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(234,plain,
( ( ! [Fa: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ! [SY1317: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ Fa ) ) @ ( sK17_SY1315 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ Fa ) @ SY1317 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ Fa ) ) @ ( sK17_SY1315 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK15_X_1 @ Fa ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ Fa ) ) )
& ! [Fa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ Fa ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
| ! [A_2: $i,B_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK14_I @ B_1 @ A_2 @ X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(235,plain,
( ( ! [Fa: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ! [SY1330: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ Fa ) @ SY1330 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ Fa ) @ SY1330 ) ) ) )
& ! [SY1331: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ Fa ) @ SY1331 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ Fa ) @ SY1331 ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK20_X_1 @ Fa ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK21_SY1318 @ Fa ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK20_X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK21_SY1318 @ Fa ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ Fa ) ) )
& ! [Fa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ Fa ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
| ! [Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Xa ) @ arrow_1834574746e_Prof ) )
| ( ! [A_2: $i,B_1: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ Xa ) ) ) )
& ! [A_2: $i,B_1: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ Xa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(236,plain,
( ( ! [X_b: $i,X_a: $i,Aa: $i,Ba: $i] :
( ! [A_4: $i,B_3: $i] :
( ( ( ti @ X_a @ Aa )
!= ( ti @ X_a @ A_4 ) )
| ( ( ti @ X_b @ Ba )
!= ( ti @ X_b @ B_3 ) )
| ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ Aa ) @ Ba )
= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_4 ) @ B_3 ) ) )
& ! [A_4: $i] :
( ! [B_3: $i] :
( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ Aa ) @ Ba )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_4 ) @ B_3 ) )
| ( ( ti @ X_a @ Aa )
= ( ti @ X_a @ A_4 ) ) )
& ! [A_4: $i,B_3: $i] :
( ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ Aa ) @ Ba )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_4 ) @ B_3 ) )
| ( ( ti @ X_b @ Ba )
= ( ti @ X_b @ B_3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(237,plain,
( ( ! [X_b: $i,X_a: $i,A_3: $i,B_2: $i] :
( ! [A_5: $i] :
( ! [B_4: $i] :
( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_3 ) @ B_2 )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_5 ) @ B_4 ) )
| ( ( ti @ X_a @ A_3 )
= ( ti @ X_a @ A_5 ) ) )
& ! [A_5: $i,B_4: $i] :
( ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_3 ) @ B_2 )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_5 ) @ B_4 ) )
| ( ( ti @ X_b @ B_2 )
= ( ti @ X_b @ B_4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(238,plain,
( ( ! [X_a: $i] :
( ! [X_b: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ ( sK26_X1 @ Pa @ X_b @ X_a ) ) )
| ! [A_2: $i,B_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_2 ) @ B_1 ) ) ) )
& ! [X_b: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK24_A_2 @ Pa @ X_b @ X_a ) ) @ ( sK25_SY1332 @ Pa @ X_b @ X_a ) ) ) )
| ! [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(239,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(240,plain,
( ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(241,plain,
( ( ! [P_1: $i,Pa: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(242,plain,
( ( ! [P_1: $i,Pa: $i,A_4: $i,B_3: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(243,plain,
( ( ! [P_1: $i,Pa: $i,Ca: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[117]) ).
thf(244,plain,
( ( ! [P_1: $i,Pa: $i,A_4: $i,B_3: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ A_4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(245,plain,
( ( ! [P_1: $i,Pa: $i,A_4: $i,B_3: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ A_4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ A_4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(246,plain,
( ( ! [X_2: $i,Y_1: $i] :
( ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(247,plain,
( ( ! [X_2: $i,Y_1: $i] :
( ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(248,plain,
( ( ( c != d ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(249,plain,
( ( ! [X_a: $i] :
( ~ ( top @ X_a )
| ( ( ti @ X_a @ ( top_top @ X_a ) )
= ( top_top @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(250,plain,
( ( ! [X_a: $i] :
( ~ ( ord @ X_a )
| ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( ord_less @ X_a ) )
= ( ord_less @ X_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(251,plain,
( ( ! [B_1_1: $i] :
( ~ ( hBOOL @ ( ti @ bool @ B_1_1 ) )
| ( hBOOL @ B_1_1 ) )
& ! [B_1_1: $i] :
( ~ ( hBOOL @ B_1_1 )
| ( hBOOL @ ( ti @ bool @ B_1_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(252,plain,
( ( ! [B_1_1: $i] :
( ~ ( hBOOL @ ( ti @ bool @ B_1_1 ) )
| ( hBOOL @ B_1_1 ) )
& ! [B_1_1: $i] :
( ~ ( hBOOL @ B_1_1 )
| ( hBOOL @ ( ti @ bool @ B_1_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(253,plain,
( ( ( ti @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ f )
= f )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(254,plain,
( ( ( ti @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ p )
= p )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(255,plain,
( ( ( ti @ arrow_1212486748le_alt @ c )
= c )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(256,plain,
( ( ( ti @ arrow_1212486748le_alt @ d )
= d )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(257,plain,
( ( ( ti @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ arrow_612047104le_IIA )
= arrow_612047104le_IIA )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(258,plain,
( ( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ arrow_638930832le_Lin )
= arrow_638930832le_Lin )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(259,plain,
( ( ( ti @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ arrow_1834574746e_Prof )
= arrow_1834574746e_Prof )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(260,plain,
( ( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ arrow_1726925404_above )
= arrow_1726925404_above )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(261,plain,
( ( ( ti @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ arrow_1990387629ctator )
= arrow_1990387629ctator )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(262,plain,
( ( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_844286440_mkbot )
= arrow_844286440_mkbot )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(263,plain,
( ( ( ti @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_992993526_mktop )
= arrow_992993526_mktop )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(264,plain,
( ( ( ti @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ arrow_1932713123nimity )
= arrow_1932713123nimity )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(265,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_b @ X_c ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) ) @ ( combb @ X_b @ X_c @ X_a ) )
= ( combb @ X_b @ X_c @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(266,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ X_b @ ( fun @ X_a @ X_c ) ) ) @ ( combc @ X_a @ X_b @ X_c ) )
= ( combc @ X_a @ X_b @ X_c ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(267,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ X_a ) @ ( combi @ X_a ) )
= ( combi @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(268,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_b @ X_a ) ) @ ( combk @ X_a @ X_b ) )
= ( combk @ X_a @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(269,plain,
( ( ! [X_a: $i,X_b: $i,X_c: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) ) @ ( combs @ X_a @ X_b @ X_c ) )
= ( combs @ X_a @ X_b @ X_c ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(270,plain,
( ( ( ti @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ nat ) @ ( finite_card @ arrow_1384031255e_indi ) )
= ( finite_card @ arrow_1384031255e_indi ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(271,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) ) @ ( inj_on @ X_a @ X_b ) )
= ( inj_on @ X_a @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(272,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) ) @ ( pi @ X_a @ X_b ) )
= ( pi @ X_a @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(273,plain,
( ( ! [X_a: $i] :
( ( ti @ X_a @ ( undefined @ X_a ) )
= ( undefined @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(274,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) ) @ ( hilbert_inv_into @ X_a @ X_b ) )
= ( hilbert_inv_into @ X_a @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(275,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ bool @ ( fun @ X_a @ ( fun @ X_a @ X_a ) ) ) @ ( if @ X_a ) )
= ( if @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(276,plain,
( ( ! [X_a: $i] :
( ~ ( ord @ X_a )
| ( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( ord_less @ X_a ) )
= ( ord_less @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(277,plain,
( ( ! [X_a: $i] :
( ~ ( top @ X_a )
| ( ( ti @ X_a @ ( top_top @ X_a ) )
= ( top_top @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(278,plain,
( ( ! [X_a: $i,X_b: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) ) @ ( product_Pair @ X_a @ X_b ) )
= ( product_Pair @ X_a @ X_b ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(279,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_b @ ( fun @ X_c @ X_a ) ) @ ( fun @ ( product_prod @ X_b @ X_c ) @ X_a ) ) @ ( product_prod_rec @ X_b @ X_c @ X_a ) )
= ( product_prod_rec @ X_b @ X_c @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(280,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) ) @ ( collect @ X_a ) )
= ( collect @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(281,plain,
( ( ( ti @ bool @ fFalse )
= fFalse )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(282,plain,
( ( ( ti @ bool @ fTrue )
= fTrue )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(283,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fequal @ X_a ) )
= ( fequal @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(284,plain,
( ( ! [X_a: $i,X_c: $i,B_1_1: $i,B_2_1: $i] :
( ( hAPP @ X_a @ X_c @ ( ti @ ( fun @ X_a @ X_c ) @ B_1_1 ) @ B_2_1 )
= ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(285,plain,
( ( ! [X_a: $i,X_c: $i,B_1_1: $i,B_2_1: $i] :
( ( hAPP @ X_a @ X_c @ B_1_1 @ ( ti @ X_a @ B_2_1 ) )
= ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(286,plain,
( ( ! [X_c: $i,X_a: $i,B_1_1: $i,B_2_1: $i] :
( ( ti @ X_c @ ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) )
= ( hAPP @ X_a @ X_c @ B_1_1 @ B_2_1 ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(287,plain,
( ( ! [X_a: $i] :
( ( ti @ ( fun @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) ) @ ( member @ X_a ) )
= ( member @ X_a ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(288,plain,
( ( ( ti @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ lab )
= lab )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(289,plain,
( ( ( ti @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ lba )
= lba )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(290,plain,
( ( ( ti @ arrow_1212486748le_alt @ a )
= a )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(291,plain,
( ( ( ti @ arrow_1212486748le_alt @ b )
= b )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(292,plain,
( ( ( ti @ arrow_1212486748le_alt @ e )
= e )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(293,plain,
( ( ( ti @ ( fun @ arrow_1384031255e_indi @ nat ) @ h )
= h )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(294,plain,
( ( ( ti @ nat @ n )
= n )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(295,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ f ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(296,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ f ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(297,plain,
( ( ( c != d ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(298,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ p ) @ arrow_1834574746e_Prof ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(299,plain,
( ( ! [X_2: $i,Y_1: $i] :
( ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(300,plain,
( ( ! [X_2: $i,Y_1: $i] :
( ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ! [L: $i,Z_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ Z_1 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Z_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(301,plain,
( ( ! [P_1: $i,Pa: $i,A_4: $i,B_3: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ A_4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK35_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ A_4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK34_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(302,plain,
( ( ! [P_1: $i,Pa: $i,A_4: $i,B_3: $i,Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ A_4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK33_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(303,plain,
( ( ! [P_1: $i,Pa: $i,Ca: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK32_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Ba )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ca ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK31_I @ Ba @ Aa @ Ca @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Ca ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(304,plain,
( ( ! [P_1: $i,Pa: $i,A_4: $i,B_3: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK30_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ A_4 )
= ( ti @ arrow_1212486748le_alt @ B_3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK29_I @ Ba @ Aa @ B_3 @ A_4 @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_4 ) @ B_3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(305,plain,
( ( ! [P_1: $i,Pa: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK28_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Pa ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ P_1 ) @ arrow_1834574746e_Prof ) )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Pa @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ P_1 @ ( sK27_I @ Ba @ Aa @ Pa @ P_1 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ P_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ Pa ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(306,plain,
( ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(307,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ ( hAPP @ nat @ arrow_1384031255e_indi @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ nat @ arrow_1384031255e_indi ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ nat @ arrow_1384031255e_indi ) ) @ ( hilbert_inv_into @ arrow_1384031255e_indi @ nat ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ) @ h ) @ n ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(308,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(309,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(310,plain,
( ( ! [X_a: $i] :
( ! [X_b: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ ( sK26_X1 @ Pa @ X_b @ X_a ) ) )
| ! [A_2: $i,B_1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_2 ) @ B_1 ) ) ) )
& ! [X_b: $i,Pa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK24_A_2 @ Pa @ X_b @ X_a ) ) @ ( sK25_SY1332 @ Pa @ X_b @ X_a ) ) ) )
| ! [X1: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ bool @ Pa @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(311,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) @ arrow_1834574746e_Prof ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(312,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ e ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(313,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(314,plain,
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ n ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ nat @ ( finite_card @ arrow_1384031255e_indi ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(315,plain,
( ( hBOOL @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ bool ) @ ( inj_on @ arrow_1384031255e_indi @ nat ) @ h ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(316,plain,
( ( ! [X_b: $i,X_a: $i,A_3: $i,B_2: $i] :
( ! [A_5: $i] :
( ! [B_4: $i] :
( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_3 ) @ B_2 )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_5 ) @ B_4 ) )
| ( ( ti @ X_a @ A_3 )
= ( ti @ X_a @ A_5 ) ) )
& ! [A_5: $i,B_4: $i] :
( ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_3 ) @ B_2 )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_5 ) @ B_4 ) )
| ( ( ti @ X_b @ B_2 )
= ( ti @ X_b @ B_4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(317,plain,
( ( ! [X_b: $i,X_a: $i,Aa: $i,Ba: $i] :
( ! [A_4: $i,B_3: $i] :
( ( ( ti @ X_a @ Aa )
!= ( ti @ X_a @ A_4 ) )
| ( ( ti @ X_b @ Ba )
!= ( ti @ X_b @ B_3 ) )
| ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ Aa ) @ Ba )
= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_4 ) @ B_3 ) ) )
& ! [A_4: $i] :
( ! [B_3: $i] :
( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ Aa ) @ Ba )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_4 ) @ B_3 ) )
| ( ( ti @ X_a @ Aa )
= ( ti @ X_a @ A_4 ) ) )
& ! [A_4: $i,B_3: $i] :
( ( ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ Aa ) @ Ba )
!= ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ A_4 ) @ B_3 ) )
| ( ( ti @ X_b @ Ba )
= ( ti @ X_b @ B_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(318,plain,
( ( ! [Fa: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ! [SY1330: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ Fa ) @ SY1330 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ Fa ) @ SY1330 ) ) ) )
& ! [SY1331: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ Fa ) @ SY1331 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ Fa ) @ SY1331 ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK20_X_1 @ Fa ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK21_SY1318 @ Fa ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK20_X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ Fa ) ) @ ( sK23_SY1327 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK21_SY1318 @ Fa ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ Fa ) ) )
& ! [Fa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ Fa ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
| ! [Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Xa ) @ arrow_1834574746e_Prof ) )
| ( ! [A_2: $i,B_1: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK19_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ Xa ) ) ) )
& ! [A_2: $i,B_1: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Xa @ ( sK18_I @ B_1 @ A_2 @ Xa @ X_1 @ Fa ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ Xa ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(319,plain,
( ( ! [Fa: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ! [SY1317: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ Fa ) ) @ ( sK17_SY1315 @ Fa ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ Fa ) @ SY1317 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ Fa ) ) @ ( sK17_SY1315 @ Fa ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK15_X_1 @ Fa ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ Fa ) ) )
& ! [Fa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ Fa ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
| ! [A_2: $i,B_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ ( sK14_I @ B_1 @ A_2 @ X_1 @ Fa ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ A_2 ) @ B_1 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(320,plain,
( ( ! [X_a: $i,X_2: $i] : ( hBOOL @ ( hAPP @ X_a @ bool @ ( top_top @ ( fun @ X_a @ bool ) ) @ X_2 ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(321,plain,
( ( ! [X_a: $i,X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(322,plain,
( ( ! [X_a: $i,X_2: $i] : ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(323,plain,
( ( ! [X_b: $i,X_c: $i,X_a: $i,F1: $i,Aa: $i,Ba: $i] :
( ( hAPP @ ( product_prod @ X_b @ X_c ) @ X_a @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ X_a ) ) @ ( fun @ ( product_prod @ X_b @ X_c ) @ X_a ) @ ( product_prod_rec @ X_b @ X_c @ X_a ) @ F1 ) @ ( hAPP @ X_c @ ( product_prod @ X_b @ X_c ) @ ( hAPP @ X_b @ ( fun @ X_c @ ( product_prod @ X_b @ X_c ) ) @ ( product_Pair @ X_b @ X_c ) @ Aa ) @ Ba ) )
= ( hAPP @ X_c @ X_a @ ( hAPP @ X_b @ ( fun @ X_c @ X_a ) @ F1 @ Aa ) @ Ba ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(324,plain,
( ( ! [X_b: $i,X_a: $i] :
( ~ ( top @ X_a )
| ! [X_2: $i] :
( ( hAPP @ X_b @ X_a @ ( top_top @ ( fun @ X_b @ X_a ) ) @ X_2 )
= ( top_top @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(325,plain,
( ( ! [X_a: $i] :
( ~ ( top @ X_a )
| ! [A_3: $i] :
~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ ( top_top @ X_a ) ) @ A_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(326,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(327,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(328,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [Z: $i,Y: $i,X: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Z ) @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Z ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(329,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [Z: $i,X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ Z ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(330,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [C: $i,B_2: $i,A_3: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) )
| ( B_2 != C )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ A_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(331,plain,
( ( ! [X_a: $i] :
( ~ ( ord @ X_a )
| ! [C: $i,A_3: $i,B_2: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) )
| ( B_2 != C )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(332,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [C: $i,A_3: $i,B_2: $i] :
( ( A_3 != B_2 )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ B_2 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ C ) @ A_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(333,plain,
( ( ! [X_a: $i] :
( ~ ( ord @ X_a )
| ! [C: $i,A_3: $i,B_2: $i] :
( ( A_3 != B_2 )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ C ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(334,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [B_2: $i,A_3: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(335,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [A_3: $i,B_2: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ A_3 ) @ B_2 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ B_2 ) @ A_3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(336,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [Pa: $i,X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( hBOOL @ Pa ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(337,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( Y != X ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(338,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( X != Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(339,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(340,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(341,plain,
( ( ! [X_a: $i] :
( ~ ( order @ X_a )
| ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( X != Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(342,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ! [X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(343,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ( ! [Y_1: $i,X_2: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) ) )
& ! [Y_1: $i,X_2: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(344,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y ) @ X ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(345,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ( ! [X_2: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(346,plain,
( ( ! [X_a: $i] :
( ~ ( linorder @ X_a )
| ( ! [X_2: $i,Y_1: $i] :
( ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X_2 ) @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) ) )
& ! [X_2: $i,Y_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Y_1 ) @ X_2 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(347,plain,
( ( ! [X_a: $i] :
( ~ ( preorder @ X_a )
| ! [X: $i] :
~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ X ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(348,plain,
( ( ! [X_a: $i] :
( ( top_top @ ( fun @ X_a @ bool ) )
= ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ ( hAPP @ bool @ ( fun @ X_a @ bool ) @ ( combk @ bool @ X_a ) @ fTrue ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(349,plain,
( ( ! [X_a: $i,X_b: $i] :
( ! [S: $i,R_1: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ R_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ S ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ R_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ ( sK12_X_1 @ R_1 @ S @ X_b @ X_a ) ) @ ( sK13_SY1311 @ R_1 @ S @ X_b @ X_a ) ) ) @ S ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S ) ) )
& ! [S: $i,R_1: $i] :
( ( ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ R_1 )
!= ( ti @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ S ) )
| ( ! [X_1: $i,Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ R_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ S ) ) )
& ! [X_1: $i,Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ S ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ X_a @ X_b ) @ ( fun @ ( fun @ ( product_prod @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( product_prod @ X_a @ X_b ) ) @ ( hAPP @ X_b @ ( product_prod @ X_a @ X_b ) @ ( hAPP @ X_a @ ( fun @ X_b @ ( product_prod @ X_a @ X_b ) ) @ ( product_Pair @ X_a @ X_b ) @ X_1 ) @ Xa ) ) @ R_1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(350,plain,
( ( ! [X_a: $i] :
( ~ ( top @ X_a )
| ( ! [Aa: $i] :
( ( ( ti @ X_a @ Aa )
= ( top_top @ X_a ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Aa ) @ ( top_top @ X_a ) ) ) )
& ! [Aa: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( ord_less @ X_a ) @ Aa ) @ ( top_top @ X_a ) ) )
| ( ( ti @ X_a @ Aa )
!= ( top_top @ X_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(351,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( ti @ X_b @ Y_1 ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F ) @ Y_1 )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(352,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(353,plain,
( ( ! [X_c: $i,X_a: $i,X_b: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ ( fun @ X_c @ X_b ) ) @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) @ ( hAPP @ ( fun @ X_b @ ( fun @ X_c @ X_b ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ ( fun @ X_c @ X_b ) ) ) @ ( combb @ X_b @ ( fun @ X_c @ X_b ) @ X_a ) @ ( combk @ X_b @ X_c ) ) @ F ) ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(354,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ A_1 ) @ F ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(355,plain,
( ( ! [X_a: $i,X_b: $i,Y_1: $i,X_2: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( ti @ X_b @ Y_1 ) )
| ( ( hAPP @ X_b @ X_a @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ A_1 ) @ F ) @ Y_1 )
= ( ti @ X_a @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(356,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i] :
( ! [Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) )
& ! [Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(357,plain,
( ( ! [X_a: $i,X_b: $i] :
( ! [F: $i,A_1: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ ( sK10_X_1 @ A_1 @ F @ X_b @ X_a ) ) @ A_1 ) )
& ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ ( sK11_SY1310 @ A_1 @ F @ X_b @ X_a ) ) @ A_1 ) )
& ( ( hAPP @ X_a @ X_b @ F @ ( sK10_X_1 @ A_1 @ F @ X_b @ X_a ) )
= ( hAPP @ X_a @ X_b @ F @ ( sK11_SY1310 @ A_1 @ F @ X_b @ X_a ) ) )
& ( ( ti @ X_a @ ( sK10_X_1 @ A_1 @ F @ X_b @ X_a ) )
!= ( ti @ X_a @ ( sK11_SY1310 @ A_1 @ F @ X_b @ X_a ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) ) )
& ! [F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_1 ) @ A_1 ) )
| ! [Xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Xa ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_1 )
!= ( hAPP @ X_a @ X_b @ F @ Xa ) )
| ( ( ti @ X_a @ X_1 )
= ( ti @ X_a @ Xa ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(358,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(359,plain,
( ( ! [X_a: $i,X_b: $i,Y_1: $i,X_2: $i] :
( ! [F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) )
& ! [F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_a @ X_2 )
!= ( ti @ X_a @ Y_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
= ( hAPP @ X_a @ X_b @ F @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(360,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ A_1 ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ Y_1 ) @ A_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(361,plain,
( ( ! [X_a: $i,A_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_a ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_a ) @ ( combi @ X_a ) ) @ A_1 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(362,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,Y_1: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ X_2 )
!= ( hAPP @ X_a @ X_b @ F @ Y_1 ) )
| ( ( ti @ X_a @ X_2 )
= ( ti @ X_a @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(363,plain,
( ( ! [X_a: $i,X_b: $i,G: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) )
| ( ( hAPP @ X_a @ X_b @ F @ ( hAPP @ X_b @ X_a @ G @ ( sK9_X_1 @ F @ G @ X_b @ X_a ) ) )
!= ( ti @ X_b @ ( sK9_X_1 @ F @ G @ X_b @ X_a ) ) )
| ( ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_b @ X_a ) ) @ ( hilbert_inv_into @ X_a @ X_b ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) @ F )
= ( ti @ ( fun @ X_b @ X_a ) @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(364,plain,
( ( ! [X_a: $i,X_b: $i,F: $i] :
( ( ( ( hAPP @ X_a @ X_b @ F @ ( sK7_X_1 @ F @ X_b @ X_a ) )
= ( hAPP @ X_a @ X_b @ F @ ( sK8_SY1309 @ F @ X_b @ X_a ) ) )
& ( ( ti @ X_a @ ( sK7_X_1 @ F @ X_b @ X_a ) )
!= ( ti @ X_a @ ( sK8_SY1309 @ F @ X_b @ X_a ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( inj_on @ X_a @ X_b ) @ F ) @ ( top_top @ ( fun @ X_a @ bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(365,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ f ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(366,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ lba ) @ arrow_638930832le_Lin ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(367,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ lab ) @ arrow_638930832le_Lin ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(368,plain,
( ( ! [Aa: $i,Ba: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Ba ) @ Aa ) ) @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(369,plain,
( ( ! [X_2: $i] :
( ! [Y_1: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Y_1 ) @ X_2 ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) )
& ! [Y_1: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Y_1 ) @ X_2 ) ) @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(370,plain,
( ( ! [X_a: $i,X_b: $i,F: $i,G: $i] :
( ( ( hAPP @ X_a @ X_b @ F @ ( sK6_X_1 @ G @ F @ X_b @ X_a ) )
!= ( hAPP @ X_a @ X_b @ G @ ( sK6_X_1 @ G @ F @ X_b @ X_a ) ) )
| ( ( ti @ ( fun @ X_a @ X_b ) @ F )
= ( ti @ ( fun @ X_a @ X_b ) @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(371,plain,
( ( ! [X_a: $i] :
( ! [X_2: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_2 ) ) )
& ! [X_2: $i,A_1: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ A_1 @ X_2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(372,plain,
( ( ! [X_a: $i,Pa: $i] :
( ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ bool ) @ ( collect @ X_a ) @ Pa )
= ( ti @ ( fun @ X_a @ bool ) @ Pa ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(373,plain,
( ( ! [X_2: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ L ) @ X_2 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(374,plain,
( ( ! [X_2: $i,L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ L ) @ X_2 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(375,plain,
( ( ! [L: $i,X_2: $i,Y_1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ X_2 ) @ Y_1 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(376,plain,
( ( ! [L: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ arrow_1384031255e_indi ) @ L ) ) @ arrow_1834574746e_Prof ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(377,plain,
( ( ! [X_2: $i,Y_1: $i,L: $i] :
( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Y_1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Y_1 ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Y_1 ) ) @ L ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
!= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Aa ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Aa ) ) @ L ) ) )
& ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ L ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ L ) @ Aa ) @ Ba ) ) )
| ( ( ti @ arrow_1212486748le_alt @ X_2 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( ti @ arrow_1212486748le_alt @ Y_1 )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ X_2 ) @ Y_1 ) ) @ L ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(378,plain,
( ( ! [I_1: $i,Fa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ Fa ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ Fa @ I_1 ) ) @ arrow_1834574746e_Prof ) )
& ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ Fa @ I_1 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ Fa @ I_1 ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ Fa @ I_1 ) ) @ ( sK5_SY1308 @ Fa @ I_1 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ Fa @ I_1 ) @ I_1 ) ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ Fa @ I_1 ) ) @ ( sK5_SY1308 @ Fa @ I_1 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK3_X_1 @ Fa @ I_1 ) ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(379,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ B ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ B @ X_2 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(380,plain,
( ( ! [Aa: $i,Ba: $i] :
( ( ( ti @ arrow_1212486748le_alt @ Aa )
= ( ti @ arrow_1212486748le_alt @ Ba ) )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ Ba @ Aa ) ) @ arrow_638930832le_Lin ) )
& ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ Aa ) @ Ba ) ) @ ( sK2_X_1 @ Ba @ Aa ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(381,plain,
( ( ! [Na: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ Na ) ) ) @ lab ) ) @ lba ) ) @ arrow_1834574746e_Prof ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(382,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ ( hAPP @ X_a @ ( fun @ X_b @ bool ) @ B @ X_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(383,plain,
( ( arrow_1834574746e_Prof
= ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( top_top @ ( fun @ arrow_1384031255e_indi @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ arrow_1384031255e_indi ) @ arrow_638930832le_Lin ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(384,plain,
( ( ! [X_a: $i,X_b: $i,X_2: $i,F: $i,A_1: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_b ) ) @ F ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ ( hAPP @ ( fun @ X_b @ bool ) @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( combk @ ( fun @ X_b @ bool ) @ X_a ) @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ X_a @ bool ) @ bool @ ( hAPP @ X_a @ ( fun @ ( fun @ X_a @ bool ) @ bool ) @ ( member @ X_a ) @ X_2 ) @ A_1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ X_b @ bool ) @ bool @ ( hAPP @ X_b @ ( fun @ ( fun @ X_b @ bool ) @ bool ) @ ( member @ X_b ) @ ( hAPP @ X_a @ X_b @ F @ X_2 ) ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(385,plain,
( ( ! [X_a: $i,A_1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) @ bool @ ( hAPP @ ( fun @ X_a @ X_a ) @ ( fun @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) @ bool ) @ ( member @ ( fun @ X_a @ X_a ) ) @ ( combi @ X_a ) ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( fun @ ( fun @ X_a @ X_a ) @ bool ) ) @ ( pi @ X_a @ X_a ) @ A_1 ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ X_a @ ( fun @ X_a @ bool ) ) @ ( combk @ ( fun @ X_a @ bool ) @ X_a ) @ A_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(386,plain,
( ( ! [Fa: $i,I_1: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ I_1 @ Fa ) ) @ arrow_1834574746e_Prof ) )
& ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ ( sK1_X_1 @ I_1 @ Fa ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ I_1 @ Fa ) @ I_1 ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) ) )
& ! [Fa: $i,I_1: $i] :
( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ Fa ) @ I_1 ) )
| ! [X_1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ X_1 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ Fa @ X_1 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ X_1 @ I_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(387,plain,
( ( ! [X_a: $i,X_b: $i,A_1: $i] :
( ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) @ ( hAPP @ ( fun @ X_a @ bool ) @ ( fun @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) @ ( pi @ X_a @ X_b ) @ A_1 ) @ ( hAPP @ ( fun @ X_b @ bool ) @ ( fun @ X_a @ ( fun @ X_b @ bool ) ) @ ( combk @ ( fun @ X_b @ bool ) @ X_a ) @ ( top_top @ ( fun @ X_b @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ X_a @ X_b ) @ bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(388,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(389,plain,
( ( ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ c ) @ e ) ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ! [I: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [I: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ I )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ I ) ) @ e ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(390,plain,
( ( ( a != b ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(391,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(392,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ a ) @ b ) ) @ lab ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(393,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ a ) @ b ) ) @ lba ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(394,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(395,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( preorder @ T_1 )
| ( preorder @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(396,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( order @ T_1 )
| ( order @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(397,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( top @ T_1 )
| ( top @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(398,plain,
( ( ! [T_2: $i,T_1: $i] :
( ~ ( ord @ T_1 )
| ( ord @ ( fun @ T_2 @ T_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(399,plain,
( ( preorder @ nat )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(400,plain,
( ( linorder @ nat )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(401,plain,
( ( order @ nat )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(402,plain,
( ( ord @ nat )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(403,plain,
( ( preorder @ bool )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(404,plain,
( ( order @ bool )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(405,plain,
( ( top @ bool )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(406,plain,
( ( ord @ bool )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(407,plain,
( ( ! [T: $i,A: $i] :
( ( ti @ T @ ( ti @ T @ A ) )
= ( ti @ T @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(408,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ( hAPP @ X_a @ X_a @ ( hAPP @ X_a @ ( fun @ X_a @ X_a ) @ ( hAPP @ bool @ ( fun @ X_a @ ( fun @ X_a @ X_a ) ) @ ( if @ X_a ) @ fTrue ) @ X ) @ Y )
= ( ti @ X_a @ X ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(409,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ( hAPP @ X_a @ X_a @ ( hAPP @ X_a @ ( fun @ X_a @ X_a ) @ ( hAPP @ bool @ ( fun @ X_a @ ( fun @ X_a @ X_a ) ) @ ( if @ X_a ) @ fFalse ) @ X ) @ Y )
= ( ti @ X_a @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(410,plain,
( ( ! [P: $i] :
( ( ( ti @ bool @ P )
= fTrue )
| ( ( ti @ bool @ P )
= fFalse ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(411,plain,
( ( ! [X_a: $i,X_c: $i,X_b: $i,P: $i,Q: $i,R: $i] :
( ( hAPP @ X_a @ X_c @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) @ ( hAPP @ ( fun @ X_b @ X_c ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) @ ( combb @ X_b @ X_c @ X_a ) @ P ) @ Q ) @ R )
= ( hAPP @ X_b @ X_c @ P @ ( hAPP @ X_a @ X_b @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(412,plain,
( ( ! [X_a: $i,X_c: $i,X_b: $i,P: $i,Q: $i,R: $i] :
( ( hAPP @ X_a @ X_c @ ( hAPP @ X_b @ ( fun @ X_a @ X_c ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ X_b @ ( fun @ X_a @ X_c ) ) @ ( combc @ X_a @ X_b @ X_c ) @ P ) @ Q ) @ R )
= ( hAPP @ X_b @ X_c @ ( hAPP @ X_a @ ( fun @ X_b @ X_c ) @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(413,plain,
( ( ! [X_a: $i,P: $i] :
( ( hAPP @ X_a @ X_a @ ( combi @ X_a ) @ P )
= ( ti @ X_a @ P ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(414,plain,
( ( ! [X_b: $i,X_a: $i,P: $i,Q: $i] :
( ( hAPP @ X_b @ X_a @ ( hAPP @ X_a @ ( fun @ X_b @ X_a ) @ ( combk @ X_a @ X_b ) @ P ) @ Q )
= ( ti @ X_a @ P ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(415,plain,
( ( ! [X_a: $i,X_c: $i,X_b: $i,P: $i,Q: $i,R: $i] :
( ( hAPP @ X_a @ X_c @ ( hAPP @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) @ ( hAPP @ ( fun @ X_a @ ( fun @ X_b @ X_c ) ) @ ( fun @ ( fun @ X_a @ X_b ) @ ( fun @ X_a @ X_c ) ) @ ( combs @ X_a @ X_b @ X_c ) @ P ) @ Q ) @ R )
= ( hAPP @ X_b @ X_c @ ( hAPP @ X_a @ ( fun @ X_b @ X_c ) @ P @ R ) @ ( hAPP @ X_a @ X_b @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(416,plain,
( ( hBOOL @ fTrue )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(417,plain,
( ( ! [P: $i] :
( ( ( ti @ bool @ P )
= fTrue )
| ( ( ti @ bool @ P )
= fFalse ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(418,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) )
| ( ( ti @ X_a @ X )
= ( ti @ X_a @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(419,plain,
( ( ! [X_a: $i,X: $i,Y: $i] :
( ( ( ti @ X_a @ X )
!= ( ti @ X_a @ Y ) )
| ( hBOOL @ ( hAPP @ X_a @ bool @ ( hAPP @ X_a @ ( fun @ X_a @ bool ) @ ( fequal @ X_a ) @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(420,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(421,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SX2 ) @ SX3 ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SX2 ) @ SX3 ) ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SX2 ) @ SX3 ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SX2 ) @ SX3 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SX2 ) @ SX3 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SX2 ) @ SX3 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX1 ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SX2 ) @ SX3 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(422,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX5 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX2 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK30_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK30_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK30_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK30_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX5 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX2 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK29_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK29_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK29_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK29_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(423,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i] :
( ! [SX5: $i] :
( ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
!= ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) )
| ( ( ti @ SX1 @ SX2 )
= ( ti @ SX1 @ SX4 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ( ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
!= ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) )
| ( ( ti @ SX0 @ SX3 )
= ( ti @ SX0 @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(424,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SX2 ) @ SX3 ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SX2 ) @ SX3 ) ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SX2 ) @ SX3 ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SX2 ) @ SX3 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SX2 ) @ SX3 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SX2 ) @ SX3 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX1 ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SX2 ) @ SX3 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(425,plain,
( ( ! [SX0: $i] :
( ~ ( linorder @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( ti @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX2 ) @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ SX2 ) )
| ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX2 ) @ SX1 ) )
| ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(426,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX1 ) @ SX0 ) ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX1 ) @ SX0 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(427,plain,
( ( ! [SX0: $i] :
( ~ ( top @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ( ( ti @ SX0 @ SX1 )
= ( top_top @ SX0 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ ( top_top @ SX0 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ ( top_top @ SX0 ) ) )
| ( ( ti @ SX0 @ SX1 )
!= ( top_top @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(428,plain,
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(429,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ! [SX1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK15_X_1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK14_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(430,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(431,plain,
( ( ! [SX0: $i] :
( ~ ( linorder @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ SX2 ) )
| ( ( ti @ SX0 @ SX2 )
!= ( ti @ SX0 @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX2 ) @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX2 ) @ SX1 ) )
| ( ( ti @ SX0 @ SX2 )
= ( ti @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(432,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SX1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SX1 @ SX0 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SX1 @ SX0 ) ) @ ( sK5_SY1308 @ SX1 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SX1 @ SX0 ) @ SX0 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SX1 @ SX0 ) ) @ ( sK5_SY1308 @ SX1 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK3_X_1 @ SX1 @ SX0 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(433,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX5 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX2 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX5 )
= ( ti @ arrow_1212486748le_alt @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK35_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK35_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK35_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK35_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX5 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX2 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX5 )
= ( ti @ arrow_1212486748le_alt @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK34_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK34_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK34_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK34_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(434,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(435,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(436,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ SX1 @ SX0 ) ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( sK2_X_1 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(437,plain,
( ( ! [SX0: $i] :
( ~ ( linorder @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( ( ti @ SX0 @ SX1 )
!= ( ti @ SX0 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ SX2 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX1 ) @ SX2 ) )
| ( ( ti @ SX0 @ SX1 )
= ( ti @ SX0 @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ ( hAPP @ SX0 @ ( fun @ SX0 @ bool ) @ ( ord_less @ SX0 ) @ SX2 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(438,plain,
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(439,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( inj_on @ SX0 @ SX1 ) @ SX4 ) @ ( top_top @ ( fun @ SX0 @ bool ) ) ) )
| ( ( hAPP @ SX0 @ SX1 @ SX4 @ SX2 )
!= ( hAPP @ SX0 @ SX1 @ SX4 @ SX3 ) )
| ( ( ti @ SX0 @ SX2 )
= ( ti @ SX0 @ SX3 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( inj_on @ SX0 @ SX1 ) @ SX4 ) @ ( top_top @ ( fun @ SX0 @ bool ) ) ) )
| ( ( ti @ SX0 @ SX2 )
!= ( ti @ SX0 @ SX3 ) )
| ( ( hAPP @ SX0 @ SX1 @ SX4 @ SX2 )
= ( hAPP @ SX0 @ SX1 @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(440,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK32_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK32_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK32_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK32_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX2 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK31_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK31_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK31_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK31_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX2 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(441,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ bool @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ SX0 @ bool @ SX2 @ SX1 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(442,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ ( sK26_X1 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i,SX4: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ ( sK24_A_2 @ SX2 @ SX1 @ SX0 ) ) @ ( sK25_SY1332 @ SX2 @ SX1 @ SX0 ) ) ) )
| ! [SX3: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ bool @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(443,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ( ( ti @ SX1 @ SX2 )
!= ( ti @ SX1 @ SX4 ) )
| ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX5 ) )
| ( ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
= ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ! [SX5: $i] :
( ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
!= ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) )
| ( ( ti @ SX1 @ SX2 )
= ( ti @ SX1 @ SX4 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ( ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX2 ) @ SX3 )
!= ( hAPP @ SX0 @ ( product_prod @ SX1 @ SX0 ) @ ( hAPP @ SX1 @ ( fun @ SX0 @ ( product_prod @ SX1 @ SX0 ) ) @ ( product_Pair @ SX1 @ SX0 ) @ SX4 ) @ SX5 ) )
| ( ( ti @ SX0 @ SX3 )
= ( ti @ SX0 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(444,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ! [SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( inj_on @ SX0 @ SX1 ) @ SX4 ) @ SX5 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ SX5 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX2 ) @ SX5 ) )
| ( ( hAPP @ SX0 @ SX1 @ SX4 @ SX3 )
!= ( hAPP @ SX0 @ SX1 @ SX4 @ SX2 ) )
| ( ( ti @ SX0 @ SX3 )
= ( ti @ SX0 @ SX2 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( inj_on @ SX0 @ SX1 ) @ SX4 ) @ SX5 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX3 ) @ SX5 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX2 ) @ SX5 ) )
| ( ( ti @ SX0 @ SX3 )
!= ( ti @ SX0 @ SX2 ) )
| ( ( hAPP @ SX0 @ SX1 @ SX4 @ SX3 )
= ( hAPP @ SX0 @ SX1 @ SX4 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(445,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ( ( hAPP @ SX0 @ SX1 @ SX2 @ ( sK7_X_1 @ SX2 @ SX1 @ SX0 ) )
!= ( hAPP @ SX0 @ SX1 @ SX2 @ ( sK8_SY1309 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ ( sK7_X_1 @ SX2 @ SX1 @ SX0 ) )
!= ( ti @ SX0 @ ( sK8_SY1309 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( inj_on @ SX0 @ SX1 ) @ SX2 ) @ ( top_top @ ( fun @ SX0 @ bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(446,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(447,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ ( sK12_X_1 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK13_SY1311 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ ( sK12_X_1 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK13_SY1311 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX2 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ ( sK12_X_1 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK13_SY1311 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ ( sK12_X_1 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ ( sK13_SY1311 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) @ SX2 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ SX3 )
= ( ti @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ SX3 )
!= ( ti @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ SX2 ) )
| ~ ( ~ ! [SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX4 ) @ SX5 ) ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX4 ) @ SX5 ) ) @ SX2 ) ) )
| ~ ! [SX4: $i,SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX4 ) @ SX5 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SX0 @ SX1 ) @ ( fun @ ( fun @ ( product_prod @ SX0 @ SX1 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SX0 @ SX1 ) ) @ ( hAPP @ SX1 @ ( product_prod @ SX0 @ SX1 ) @ ( hAPP @ SX0 @ ( fun @ SX1 @ ( product_prod @ SX0 @ SX1 ) ) @ ( product_Pair @ SX0 @ SX1 ) @ SX4 ) @ SX5 ) ) @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(448,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ ( sK10_X_1 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ ( sK11_SY1310 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 ) )
| ~ ~ ( ( ( hAPP @ SX0 @ SX1 @ SX2 @ ( sK10_X_1 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( hAPP @ SX0 @ SX1 @ SX2 @ ( sK11_SY1310 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( ( ti @ SX0 @ ( sK10_X_1 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( ti @ SX0 @ ( sK11_SY1310 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( inj_on @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ ( fun @ SX0 @ SX1 ) @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( inj_on @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) )
| ! [SX4: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX4 ) @ SX3 ) )
| ! [SX5: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SX0 @ bool ) @ bool @ ( hAPP @ SX0 @ ( fun @ ( fun @ SX0 @ bool ) @ bool ) @ ( member @ SX0 ) @ SX5 ) @ SX3 ) )
| ( ( hAPP @ SX0 @ SX1 @ SX2 @ SX4 )
!= ( hAPP @ SX0 @ SX1 @ SX2 @ SX5 ) )
| ( ( ti @ SX0 @ SX4 )
= ( ti @ SX0 @ SX5 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(449,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX3 ) ) @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX3 ) ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX3 ) ) @ SX2 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX3 ) ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX1 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX1 ) ) @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
!= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX3 ) ) @ SX2 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX3 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SX2 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SX2 ) @ SX3 ) @ SX4 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SX0 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX1 )
= ( ti @ arrow_1212486748le_alt @ SX4 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX0 ) @ SX1 ) ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(450,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX2 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK28_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK28_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK28_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK28_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX2 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX2 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK27_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK27_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK27_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX2 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK27_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX2 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(451,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX5 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX2 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX4 )
= ( ti @ arrow_1212486748le_alt @ SX3 ) )
| ( ( ti @ arrow_1212486748le_alt @ SX5 )
= ( ti @ arrow_1212486748le_alt @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX0 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK33_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK33_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK33_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK33_I @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX4 ) @ SX5 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(452,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SX1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK1_X_1 @ SX1 @ SX0 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(453,plain,
! [SV1: $i] :
( ( ! [SY1333: $i,SY1334: $i] :
( ( ti @ ( fun @ ( fun @ SV1 @ SY1333 ) @ ( fun @ ( fun @ SY1334 @ SV1 ) @ ( fun @ SY1334 @ SY1333 ) ) ) @ ( combb @ SV1 @ SY1333 @ SY1334 ) )
= ( combb @ SV1 @ SY1333 @ SY1334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(454,plain,
! [SV2: $i] :
( ( ! [SY1335: $i,SY1336: $i] :
( ( ti @ ( fun @ ( fun @ SV2 @ ( fun @ SY1335 @ SY1336 ) ) @ ( fun @ SY1335 @ ( fun @ SV2 @ SY1336 ) ) ) @ ( combc @ SV2 @ SY1335 @ SY1336 ) )
= ( combc @ SV2 @ SY1335 @ SY1336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(455,plain,
! [SV3: $i] :
( ( ( ti @ ( fun @ SV3 @ SV3 ) @ ( combi @ SV3 ) )
= ( combi @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(456,plain,
! [SV4: $i] :
( ( ! [SY1337: $i] :
( ( ti @ ( fun @ SV4 @ ( fun @ SY1337 @ SV4 ) ) @ ( combk @ SV4 @ SY1337 ) )
= ( combk @ SV4 @ SY1337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(457,plain,
! [SV5: $i] :
( ( ! [SY1338: $i,SY1339: $i] :
( ( ti @ ( fun @ ( fun @ SV5 @ ( fun @ SY1338 @ SY1339 ) ) @ ( fun @ ( fun @ SV5 @ SY1338 ) @ ( fun @ SV5 @ SY1339 ) ) ) @ ( combs @ SV5 @ SY1338 @ SY1339 ) )
= ( combs @ SV5 @ SY1338 @ SY1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(458,plain,
! [SV6: $i] :
( ( ! [SY1340: $i] :
( ( ti @ ( fun @ ( fun @ SV6 @ SY1340 ) @ ( fun @ ( fun @ SV6 @ bool ) @ bool ) ) @ ( inj_on @ SV6 @ SY1340 ) )
= ( inj_on @ SV6 @ SY1340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(459,plain,
! [SV7: $i] :
( ( ! [SY1341: $i] :
( ( ti @ ( fun @ ( fun @ SV7 @ bool ) @ ( fun @ ( fun @ SV7 @ ( fun @ SY1341 @ bool ) ) @ ( fun @ ( fun @ SV7 @ SY1341 ) @ bool ) ) ) @ ( pi @ SV7 @ SY1341 ) )
= ( pi @ SV7 @ SY1341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(460,plain,
! [SV8: $i] :
( ( ( ti @ SV8 @ ( undefined @ SV8 ) )
= ( undefined @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(461,plain,
! [SV9: $i] :
( ( ! [SY1342: $i] :
( ( ti @ ( fun @ ( fun @ SV9 @ bool ) @ ( fun @ ( fun @ SV9 @ SY1342 ) @ ( fun @ SY1342 @ SV9 ) ) ) @ ( hilbert_inv_into @ SV9 @ SY1342 ) )
= ( hilbert_inv_into @ SV9 @ SY1342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(462,plain,
! [SV10: $i] :
( ( ( ti @ ( fun @ bool @ ( fun @ SV10 @ ( fun @ SV10 @ SV10 ) ) ) @ ( if @ SV10 ) )
= ( if @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(463,plain,
! [SV11: $i] :
( ( ~ ( ord @ SV11 )
| ( ( ti @ ( fun @ SV11 @ ( fun @ SV11 @ bool ) ) @ ( ord_less @ SV11 ) )
= ( ord_less @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(464,plain,
! [SV12: $i] :
( ( ~ ( top @ SV12 )
| ( ( ti @ SV12 @ ( top_top @ SV12 ) )
= ( top_top @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(465,plain,
! [SV13: $i] :
( ( ! [SY1343: $i] :
( ( ti @ ( fun @ SV13 @ ( fun @ SY1343 @ ( product_prod @ SV13 @ SY1343 ) ) ) @ ( product_Pair @ SV13 @ SY1343 ) )
= ( product_Pair @ SV13 @ SY1343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(466,plain,
! [SV14: $i] :
( ( ! [SY1344: $i,SY1345: $i] :
( ( ti @ ( fun @ ( fun @ SV14 @ ( fun @ SY1344 @ SY1345 ) ) @ ( fun @ ( product_prod @ SV14 @ SY1344 ) @ SY1345 ) ) @ ( product_prod_rec @ SV14 @ SY1344 @ SY1345 ) )
= ( product_prod_rec @ SV14 @ SY1344 @ SY1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(467,plain,
! [SV15: $i] :
( ( ( ti @ ( fun @ ( fun @ SV15 @ bool ) @ ( fun @ SV15 @ bool ) ) @ ( collect @ SV15 ) )
= ( collect @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(468,plain,
! [SV16: $i] :
( ( ( ti @ ( fun @ SV16 @ ( fun @ SV16 @ bool ) ) @ ( fequal @ SV16 ) )
= ( fequal @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(469,plain,
! [SV17: $i] :
( ( ! [SY1346: $i,SY1347: $i,SY1348: $i] :
( ( hAPP @ SV17 @ SY1346 @ ( ti @ ( fun @ SV17 @ SY1346 ) @ SY1347 ) @ SY1348 )
= ( hAPP @ SV17 @ SY1346 @ SY1347 @ SY1348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(470,plain,
! [SV18: $i] :
( ( ! [SY1349: $i,SY1350: $i,SY1351: $i] :
( ( hAPP @ SV18 @ SY1349 @ SY1350 @ ( ti @ SV18 @ SY1351 ) )
= ( hAPP @ SV18 @ SY1349 @ SY1350 @ SY1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(471,plain,
! [SV19: $i] :
( ( ! [SY1352: $i,SY1353: $i,SY1354: $i] :
( ( ti @ SV19 @ ( hAPP @ SY1352 @ SV19 @ SY1353 @ SY1354 ) )
= ( hAPP @ SY1352 @ SV19 @ SY1353 @ SY1354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(472,plain,
! [SV20: $i] :
( ( ( ti @ ( fun @ SV20 @ ( fun @ ( fun @ SV20 @ bool ) @ bool ) ) @ ( member @ SV20 ) )
= ( member @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(473,plain,
( ( c = d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(474,plain,
! [SV21: $i] :
( ( ! [SY1355: $i] : ( hBOOL @ ( hAPP @ SV21 @ bool @ ( top_top @ ( fun @ SV21 @ bool ) ) @ SY1355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(475,plain,
! [SV22: $i] :
( ( ! [SY1356: $i] : ( hBOOL @ ( hAPP @ ( fun @ SV22 @ bool ) @ bool @ ( hAPP @ SV22 @ ( fun @ ( fun @ SV22 @ bool ) @ bool ) @ ( member @ SV22 ) @ SY1356 ) @ ( top_top @ ( fun @ SV22 @ bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(476,plain,
! [SV23: $i] :
( ( ! [SY1357: $i] : ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SY1357 ) @ ( top_top @ ( fun @ SV23 @ bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(477,plain,
! [SV24: $i] :
( ( ! [SY1358: $i,SY1359: $i,SY1360: $i,SY1361: $i,SY1362: $i] :
( ( hAPP @ ( product_prod @ SV24 @ SY1358 ) @ SY1359 @ ( hAPP @ ( fun @ SV24 @ ( fun @ SY1358 @ SY1359 ) ) @ ( fun @ ( product_prod @ SV24 @ SY1358 ) @ SY1359 ) @ ( product_prod_rec @ SV24 @ SY1358 @ SY1359 ) @ SY1360 ) @ ( hAPP @ SY1358 @ ( product_prod @ SV24 @ SY1358 ) @ ( hAPP @ SV24 @ ( fun @ SY1358 @ ( product_prod @ SV24 @ SY1358 ) ) @ ( product_Pair @ SV24 @ SY1358 ) @ SY1361 ) @ SY1362 ) )
= ( hAPP @ SY1358 @ SY1359 @ ( hAPP @ SV24 @ ( fun @ SY1358 @ SY1359 ) @ SY1360 @ SY1361 ) @ SY1362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(478,plain,
! [SV25: $i] :
( ( ! [SY1363: $i] :
( ~ ( top @ SY1363 )
| ! [SY1364: $i] :
( ( hAPP @ SV25 @ SY1363 @ ( top_top @ ( fun @ SV25 @ SY1363 ) ) @ SY1364 )
= ( top_top @ SY1363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(479,plain,
! [SV26: $i] :
( ( ~ ( top @ SV26 )
| ! [SY1365: $i] :
~ ( hBOOL @ ( hAPP @ SV26 @ bool @ ( hAPP @ SV26 @ ( fun @ SV26 @ bool ) @ ( ord_less @ SV26 ) @ ( top_top @ SV26 ) ) @ SY1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(480,plain,
! [SV27: $i] :
( ( ~ ( linorder @ SV27 )
| ! [SY1366: $i,SY1367: $i] :
( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SY1366 ) @ SY1367 ) )
| ( ( ti @ SV27 @ SY1366 )
= ( ti @ SV27 @ SY1367 ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SY1367 ) @ SY1366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(481,plain,
! [SV28: $i] :
( ( ~ ( preorder @ SV28 )
| ! [SY1368: $i,SY1369: $i] :
( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SY1368 ) @ SY1369 ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SY1369 ) @ SY1368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(482,plain,
! [SV29: $i] :
( ( ~ ( order @ SV29 )
| ! [SY1370: $i,SY1371: $i,SY1372: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1371 ) @ SY1372 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1370 ) @ SY1371 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1370 ) @ SY1372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(483,plain,
! [SV30: $i] :
( ( ~ ( preorder @ SV30 )
| ! [SY1373: $i,SY1374: $i,SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1374 ) @ SY1375 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1375 ) @ SY1373 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1374 ) @ SY1373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(484,plain,
! [SV31: $i] :
( ( ~ ( order @ SV31 )
| ! [SY1376: $i,SY1377: $i,SY1378: $i] :
( ~ ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SY1377 ) @ SY1378 ) )
| ( SY1377 != SY1376 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SY1376 ) @ SY1378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(485,plain,
! [SV32: $i] :
( ( ~ ( ord @ SV32 )
| ! [SY1379: $i,SY1380: $i,SY1381: $i] :
( ~ ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY1380 ) @ SY1381 ) )
| ( SY1381 != SY1379 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY1380 ) @ SY1379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(486,plain,
! [SV33: $i] :
( ( ~ ( order @ SV33 )
| ! [SY1382: $i,SY1383: $i,SY1384: $i] :
( ( SY1383 != SY1384 )
| ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SY1382 ) @ SY1384 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SY1382 ) @ SY1383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(487,plain,
! [SV34: $i] :
( ( ~ ( ord @ SV34 )
| ! [SY1385: $i,SY1386: $i,SY1387: $i] :
( ( SY1386 != SY1387 )
| ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY1387 ) @ SY1385 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY1386 ) @ SY1385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(488,plain,
! [SV35: $i] :
( ( ~ ( order @ SV35 )
| ! [SY1388: $i,SY1389: $i] :
( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SY1388 ) @ SY1389 ) )
| ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SY1389 ) @ SY1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(489,plain,
! [SV36: $i] :
( ( ~ ( preorder @ SV36 )
| ! [SY1390: $i,SY1391: $i] :
( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SY1390 ) @ SY1391 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SY1391 ) @ SY1390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(490,plain,
! [SV37: $i] :
( ( ~ ( preorder @ SV37 )
| ! [SY1392: $i,SY1393: $i,SY1394: $i] :
( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY1393 ) @ SY1394 ) )
| ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY1394 ) @ SY1393 ) )
| ( hBOOL @ SY1392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(491,plain,
! [SV38: $i] :
( ( ~ ( order @ SV38 )
| ! [SY1395: $i,SY1396: $i] :
( ~ ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SY1395 ) @ SY1396 ) )
| ( SY1396 != SY1395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(492,plain,
! [SV39: $i] :
( ( ~ ( order @ SV39 )
| ! [SY1397: $i,SY1398: $i] :
( ~ ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SY1397 ) @ SY1398 ) )
| ( SY1397 != SY1398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(493,plain,
! [SV40: $i] :
( ( ~ ( preorder @ SV40 )
| ! [SY1399: $i,SY1400: $i] :
( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SY1399 ) @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SY1400 ) @ SY1399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(494,plain,
! [SV41: $i] :
( ( ~ ( preorder @ SV41 )
| ! [SY1401: $i,SY1402: $i] :
( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SY1401 ) @ SY1402 ) )
| ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SY1402 ) @ SY1401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(495,plain,
! [SV42: $i] :
( ( ~ ( order @ SV42 )
| ! [SY1403: $i,SY1404: $i] :
( ~ ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SY1403 ) @ SY1404 ) )
| ( SY1403 != SY1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(496,plain,
! [SV43: $i] :
( ( ~ ( linorder @ SV43 )
| ! [SY1405: $i,SY1406: $i] :
( ( ( ti @ SV43 @ SY1405 )
= ( ti @ SV43 @ SY1406 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SY1405 ) @ SY1406 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SY1406 ) @ SY1405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(497,plain,
! [SV44: $i] :
( ( ~ ( linorder @ SV44 )
| ! [SY1407: $i,SY1408: $i] :
( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SY1408 ) @ SY1407 ) )
| ( ( ti @ SV44 @ SY1407 )
= ( ti @ SV44 @ SY1408 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SY1407 ) @ SY1408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(498,plain,
! [SV45: $i] :
( ( ~ ( preorder @ SV45 )
| ! [SY1409: $i] :
~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( ord_less @ SV45 ) @ SY1409 ) @ SY1409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(499,plain,
! [SV46: $i] :
( ( ( top_top @ ( fun @ SV46 @ bool ) )
= ( hAPP @ ( fun @ SV46 @ bool ) @ ( fun @ SV46 @ bool ) @ ( collect @ SV46 ) @ ( hAPP @ bool @ ( fun @ SV46 @ bool ) @ ( combk @ bool @ SV46 ) @ fTrue ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(500,plain,
! [SV47: $i] :
( ( ! [SY1410: $i,SY1411: $i,SY1412: $i,SY1413: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SY1410 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SY1410 ) @ SY1413 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
| ( ( hAPP @ SV47 @ SY1410 @ SY1413 @ SY1411 )
!= ( ti @ SY1410 @ SY1412 ) )
| ( ( hAPP @ SY1410 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SY1410 ) @ ( fun @ SY1410 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SY1410 ) @ ( fun @ SY1410 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SY1410 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SY1413 ) @ SY1412 )
= ( ti @ SV47 @ SY1411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(501,plain,
! [SV48: $i] :
( ( ! [SY1414: $i,SY1415: $i,SY1416: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV48 @ bool ) @ bool @ ( hAPP @ ( fun @ SV48 @ SY1414 ) @ ( fun @ ( fun @ SV48 @ bool ) @ bool ) @ ( inj_on @ SV48 @ SY1414 ) @ SY1416 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) )
| ( ( hAPP @ SY1414 @ SV48 @ ( hAPP @ ( fun @ SV48 @ SY1414 ) @ ( fun @ SY1414 @ SV48 ) @ ( hAPP @ ( fun @ SV48 @ bool ) @ ( fun @ ( fun @ SV48 @ SY1414 ) @ ( fun @ SY1414 @ SV48 ) ) @ ( hilbert_inv_into @ SV48 @ SY1414 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) @ SY1416 ) @ ( hAPP @ SV48 @ SY1414 @ SY1416 @ SY1415 ) )
= ( ti @ SV48 @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(502,plain,
! [SV49: $i] :
( ( ! [SY1417: $i,SY1418: $i,SY1419: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SY1417 @ bool ) @ bool @ ( hAPP @ ( fun @ SY1417 @ SY1418 ) @ ( fun @ ( fun @ SY1417 @ bool ) @ bool ) @ ( inj_on @ SY1417 @ SY1418 ) @ SY1419 ) @ ( top_top @ ( fun @ SY1417 @ bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SY1417 @ bool ) @ bool @ ( hAPP @ ( fun @ SY1417 @ ( fun @ SV49 @ SY1418 ) ) @ ( fun @ ( fun @ SY1417 @ bool ) @ bool ) @ ( inj_on @ SY1417 @ ( fun @ SV49 @ SY1418 ) ) @ ( hAPP @ ( fun @ SY1417 @ SY1418 ) @ ( fun @ SY1417 @ ( fun @ SV49 @ SY1418 ) ) @ ( hAPP @ ( fun @ SY1418 @ ( fun @ SV49 @ SY1418 ) ) @ ( fun @ ( fun @ SY1417 @ SY1418 ) @ ( fun @ SY1417 @ ( fun @ SV49 @ SY1418 ) ) ) @ ( combb @ SY1418 @ ( fun @ SV49 @ SY1418 ) @ SY1417 ) @ ( combk @ SY1418 @ SV49 ) ) @ SY1419 ) ) @ ( top_top @ ( fun @ SY1417 @ bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(503,plain,
! [SV50: $i] :
( ( ! [SY1420: $i,SY1421: $i,SY1422: $i,SY1423: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SY1420 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SY1420 ) @ SY1422 ) @ SY1423 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SY1421 ) @ SY1423 ) )
| ( ( hAPP @ SY1420 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SY1420 ) @ ( fun @ SY1420 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SY1420 ) @ ( fun @ SY1420 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SY1420 ) @ SY1423 ) @ SY1422 ) @ ( hAPP @ SV50 @ SY1420 @ SY1422 @ SY1421 ) )
= ( ti @ SV50 @ SY1421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(504,plain,
! [SV51: $i] :
( ( ! [SY1424: $i,SY1425: $i,SY1426: $i,SY1427: $i,SY1428: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SY1424 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SY1424 ) @ SY1427 ) @ SY1428 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SY1426 ) @ SY1428 ) )
| ( ( hAPP @ SV51 @ SY1424 @ SY1427 @ SY1426 )
!= ( ti @ SY1424 @ SY1425 ) )
| ( ( hAPP @ SY1424 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SY1424 ) @ ( fun @ SY1424 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SY1424 ) @ ( fun @ SY1424 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SY1424 ) @ SY1428 ) @ SY1427 ) @ SY1425 )
= ( ti @ SV51 @ SY1426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(505,plain,
! [SV52: $i] :
( ( ! [SY1429: $i,SY1430: $i,SY1431: $i,SY1432: $i,SY1433: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SY1429 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SY1429 ) @ SY1432 ) @ SY1433 ) )
| ( ( ti @ SV52 @ SY1430 )
= ( ti @ SV52 @ SY1431 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SY1430 ) @ SY1433 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SY1431 ) @ SY1433 ) )
| ( ( hAPP @ SV52 @ SY1429 @ SY1432 @ SY1430 )
!= ( hAPP @ SV52 @ SY1429 @ SY1432 @ SY1431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(506,plain,
! [SV53: $i] :
( ( ! [SY1434: $i,SY1435: $i,SY1436: $i,SY1437: $i,SY1438: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SY1434 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SY1434 ) @ SY1437 ) @ SY1438 ) )
| ( ( hAPP @ SV53 @ SY1434 @ SY1437 @ SY1435 )
!= ( hAPP @ SV53 @ SY1434 @ SY1437 @ SY1436 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SY1435 ) @ SY1438 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SY1436 ) @ SY1438 ) )
| ( ( ti @ SV53 @ SY1435 )
= ( ti @ SV53 @ SY1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(507,plain,
! [SV54: $i] :
( ( ! [SY1439: $i] : ( hBOOL @ ( hAPP @ ( fun @ SV54 @ bool ) @ bool @ ( hAPP @ ( fun @ SV54 @ SV54 ) @ ( fun @ ( fun @ SV54 @ bool ) @ bool ) @ ( inj_on @ SV54 @ SV54 ) @ ( combi @ SV54 ) ) @ SY1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(508,plain,
! [SV55: $i] :
( ( ! [SY1440: $i,SY1441: $i,SY1442: $i,SY1443: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SY1440 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SY1440 ) @ SY1443 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
| ( ( hAPP @ SV55 @ SY1440 @ SY1443 @ SY1441 )
!= ( hAPP @ SV55 @ SY1440 @ SY1443 @ SY1442 ) )
| ( ( ti @ SV55 @ SY1441 )
= ( ti @ SV55 @ SY1442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(509,plain,
! [SV56: $i] :
( ( ! [SY1444: $i,SY1445: $i,SY1446: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SY1444 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SY1444 ) @ SY1446 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) )
| ( ( hAPP @ SV56 @ SY1444 @ SY1446 @ ( hAPP @ SY1444 @ SV56 @ SY1445 @ ( sK9_X_1 @ SY1446 @ SY1445 @ SY1444 @ SV56 ) ) )
!= ( ti @ SY1444 @ ( sK9_X_1 @ SY1446 @ SY1445 @ SY1444 @ SV56 ) ) )
| ( ( hAPP @ ( fun @ SV56 @ SY1444 ) @ ( fun @ SY1444 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SY1444 ) @ ( fun @ SY1444 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SY1444 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SY1446 )
= ( ti @ ( fun @ SY1444 @ SV56 ) @ SY1445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(510,plain,
! [SV57: $i] :
( ( ! [SY1447: $i,SY1448: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1448 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SY1447 ) ) @ SY1448 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1447 ) @ SV57 ) ) @ SY1448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(511,plain,
! [SV58: $i] :
( ( ! [SY1449: $i,SY1450: $i,SY1451: $i] :
( ( ( hAPP @ SV58 @ SY1449 @ SY1450 @ ( sK6_X_1 @ SY1451 @ SY1450 @ SY1449 @ SV58 ) )
!= ( hAPP @ SV58 @ SY1449 @ SY1451 @ ( sK6_X_1 @ SY1451 @ SY1450 @ SY1449 @ SV58 ) ) )
| ( ( ti @ ( fun @ SV58 @ SY1449 ) @ SY1450 )
= ( ti @ ( fun @ SV58 @ SY1449 ) @ SY1451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(512,plain,
! [SV59: $i] :
( ( ! [SY1452: $i] :
( ( hAPP @ ( fun @ SV59 @ bool ) @ ( fun @ SV59 @ bool ) @ ( collect @ SV59 ) @ SY1452 )
= ( ti @ ( fun @ SV59 @ bool ) @ SY1452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(513,plain,
! [SV60: $i] :
( ( ! [SY1453: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1453 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1453 ) @ SV60 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(514,plain,
! [SV61: $i] :
( ( ! [SY1454: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1454 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1454 ) @ SV61 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(515,plain,
! [SV62: $i] :
( ( ! [SY1455: $i,SY1456: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1455 )
= ( ti @ arrow_1212486748le_alt @ SY1456 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV62 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV62 ) @ SY1455 ) @ SY1456 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(516,plain,
! [SV63: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV63 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ arrow_1384031255e_indi ) @ SV63 ) ) @ arrow_1834574746e_Prof ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(517,plain,
! [SV64: $i] :
( ( ! [SY1457: $i,SY1458: $i,SY1459: $i,SY1460: $i,SY1461: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SY1457 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SY1457 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SY1457 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SY1457 ) ) @ SY1459 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SY1457 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SY1457 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SY1457 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SY1457 ) @ bool ) ) @ ( pi @ SV64 @ SY1457 ) @ SY1460 ) @ SY1461 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SY1457 @ bool ) @ bool @ ( hAPP @ SY1457 @ ( fun @ ( fun @ SY1457 @ bool ) @ bool ) @ ( member @ SY1457 ) @ ( hAPP @ SV64 @ SY1457 @ SY1459 @ SY1458 ) ) @ ( hAPP @ SV64 @ ( fun @ SY1457 @ bool ) @ SY1461 @ SY1458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SY1458 ) @ SY1460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(518,plain,
! [SV65: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ SV65 ) ) ) @ lab ) ) @ lba ) ) @ arrow_1834574746e_Prof ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(519,plain,
! [SV66: $i] :
( ( ! [SY1462: $i,SY1463: $i,SY1464: $i,SY1465: $i,SY1466: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SY1462 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SY1462 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SY1462 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SY1462 ) ) @ SY1464 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SY1462 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SY1462 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SY1462 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SY1462 ) @ bool ) ) @ ( pi @ SV66 @ SY1462 ) @ SY1465 ) @ SY1466 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SY1463 ) @ SY1465 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SY1462 @ bool ) @ bool @ ( hAPP @ SY1462 @ ( fun @ ( fun @ SY1462 @ bool ) @ bool ) @ ( member @ SY1462 ) @ ( hAPP @ SV66 @ SY1462 @ SY1464 @ SY1463 ) ) @ ( hAPP @ SV66 @ ( fun @ SY1462 @ bool ) @ SY1466 @ SY1463 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(520,plain,
! [SV67: $i] :
( ( ! [SY1467: $i,SY1468: $i,SY1469: $i,SY1470: $i,SY1471: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SY1467 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SY1467 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SY1467 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SY1467 ) ) @ SY1469 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SY1467 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SY1467 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SY1467 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SY1467 ) @ bool ) ) @ ( pi @ SV67 @ SY1467 ) @ SY1470 ) @ ( hAPP @ ( fun @ SY1467 @ bool ) @ ( fun @ SV67 @ ( fun @ SY1467 @ bool ) ) @ ( combk @ ( fun @ SY1467 @ bool ) @ SV67 ) @ SY1471 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SY1468 ) @ SY1470 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SY1467 @ bool ) @ bool @ ( hAPP @ SY1467 @ ( fun @ ( fun @ SY1467 @ bool ) @ bool ) @ ( member @ SY1467 ) @ ( hAPP @ SV67 @ SY1467 @ SY1469 @ SY1468 ) ) @ SY1471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(521,plain,
! [SV68: $i] :
( ( ! [SY1472: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV68 @ SV68 ) @ ( fun @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV68 @ SV68 ) ) @ ( combi @ SV68 ) ) @ ( hAPP @ ( fun @ SV68 @ ( fun @ SV68 @ bool ) ) @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) @ ( hAPP @ ( fun @ SV68 @ bool ) @ ( fun @ ( fun @ SV68 @ ( fun @ SV68 @ bool ) ) @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) ) @ ( pi @ SV68 @ SV68 ) @ SY1472 ) @ ( hAPP @ ( fun @ SV68 @ bool ) @ ( fun @ SV68 @ ( fun @ SV68 @ bool ) ) @ ( combk @ ( fun @ SV68 @ bool ) @ SV68 ) @ SY1472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(522,plain,
! [SV69: $i] :
( ( ! [SY1473: $i,SY1474: $i] :
( ( hAPP @ ( fun @ SV69 @ ( fun @ SY1473 @ bool ) ) @ ( fun @ ( fun @ SV69 @ SY1473 ) @ bool ) @ ( hAPP @ ( fun @ SV69 @ bool ) @ ( fun @ ( fun @ SV69 @ ( fun @ SY1473 @ bool ) ) @ ( fun @ ( fun @ SV69 @ SY1473 ) @ bool ) ) @ ( pi @ SV69 @ SY1473 ) @ SY1474 ) @ ( hAPP @ ( fun @ SY1473 @ bool ) @ ( fun @ SV69 @ ( fun @ SY1473 @ bool ) ) @ ( combk @ ( fun @ SY1473 @ bool ) @ SV69 ) @ ( top_top @ ( fun @ SY1473 @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ SV69 @ SY1473 ) @ bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(523,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(524,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ a ) @ b ) ) @ lba ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(525,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(526,plain,
! [SV70: $i] :
( ( ! [SY1475: $i] :
( ~ ( preorder @ SY1475 )
| ( preorder @ ( fun @ SV70 @ SY1475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(527,plain,
! [SV71: $i] :
( ( ! [SY1476: $i] :
( ~ ( order @ SY1476 )
| ( order @ ( fun @ SV71 @ SY1476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(528,plain,
! [SV72: $i] :
( ( ! [SY1477: $i] :
( ~ ( top @ SY1477 )
| ( top @ ( fun @ SV72 @ SY1477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(529,plain,
! [SV73: $i] :
( ( ! [SY1478: $i] :
( ~ ( ord @ SY1478 )
| ( ord @ ( fun @ SV73 @ SY1478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(530,plain,
! [SV74: $i] :
( ( ! [SY1479: $i] :
( ( ti @ SV74 @ ( ti @ SV74 @ SY1479 ) )
= ( ti @ SV74 @ SY1479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(531,plain,
! [SV75: $i] :
( ( ! [SY1480: $i,SY1481: $i] :
( ( hAPP @ SV75 @ SV75 @ ( hAPP @ SV75 @ ( fun @ SV75 @ SV75 ) @ ( hAPP @ bool @ ( fun @ SV75 @ ( fun @ SV75 @ SV75 ) ) @ ( if @ SV75 ) @ fTrue ) @ SY1480 ) @ SY1481 )
= ( ti @ SV75 @ SY1480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(532,plain,
! [SV76: $i] :
( ( ! [SY1482: $i,SY1483: $i] :
( ( hAPP @ SV76 @ SV76 @ ( hAPP @ SV76 @ ( fun @ SV76 @ SV76 ) @ ( hAPP @ bool @ ( fun @ SV76 @ ( fun @ SV76 @ SV76 ) ) @ ( if @ SV76 ) @ fFalse ) @ SY1482 ) @ SY1483 )
= ( ti @ SV76 @ SY1483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(533,plain,
! [SV77: $i] :
( ( ( ( ti @ bool @ SV77 )
= fTrue )
| ( ( ti @ bool @ SV77 )
= fFalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(534,plain,
! [SV78: $i] :
( ( ! [SY1484: $i,SY1485: $i,SY1486: $i,SY1487: $i,SY1488: $i] :
( ( hAPP @ SV78 @ SY1484 @ ( hAPP @ ( fun @ SV78 @ SY1485 ) @ ( fun @ SV78 @ SY1484 ) @ ( hAPP @ ( fun @ SY1485 @ SY1484 ) @ ( fun @ ( fun @ SV78 @ SY1485 ) @ ( fun @ SV78 @ SY1484 ) ) @ ( combb @ SY1485 @ SY1484 @ SV78 ) @ SY1486 ) @ SY1487 ) @ SY1488 )
= ( hAPP @ SY1485 @ SY1484 @ SY1486 @ ( hAPP @ SV78 @ SY1485 @ SY1487 @ SY1488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(535,plain,
! [SV79: $i] :
( ( ! [SY1489: $i,SY1490: $i,SY1491: $i,SY1492: $i,SY1493: $i] :
( ( hAPP @ SV79 @ SY1489 @ ( hAPP @ SY1490 @ ( fun @ SV79 @ SY1489 ) @ ( hAPP @ ( fun @ SV79 @ ( fun @ SY1490 @ SY1489 ) ) @ ( fun @ SY1490 @ ( fun @ SV79 @ SY1489 ) ) @ ( combc @ SV79 @ SY1490 @ SY1489 ) @ SY1491 ) @ SY1492 ) @ SY1493 )
= ( hAPP @ SY1490 @ SY1489 @ ( hAPP @ SV79 @ ( fun @ SY1490 @ SY1489 ) @ SY1491 @ SY1493 ) @ SY1492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(536,plain,
! [SV80: $i] :
( ( ! [SY1494: $i] :
( ( hAPP @ SV80 @ SV80 @ ( combi @ SV80 ) @ SY1494 )
= ( ti @ SV80 @ SY1494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(537,plain,
! [SV81: $i] :
( ( ! [SY1495: $i,SY1496: $i,SY1497: $i] :
( ( hAPP @ SV81 @ SY1495 @ ( hAPP @ SY1495 @ ( fun @ SV81 @ SY1495 ) @ ( combk @ SY1495 @ SV81 ) @ SY1496 ) @ SY1497 )
= ( ti @ SY1495 @ SY1496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(538,plain,
! [SV82: $i] :
( ( ! [SY1498: $i,SY1499: $i,SY1500: $i,SY1501: $i,SY1502: $i] :
( ( hAPP @ SV82 @ SY1498 @ ( hAPP @ ( fun @ SV82 @ SY1499 ) @ ( fun @ SV82 @ SY1498 ) @ ( hAPP @ ( fun @ SV82 @ ( fun @ SY1499 @ SY1498 ) ) @ ( fun @ ( fun @ SV82 @ SY1499 ) @ ( fun @ SV82 @ SY1498 ) ) @ ( combs @ SV82 @ SY1499 @ SY1498 ) @ SY1500 ) @ SY1501 ) @ SY1502 )
= ( hAPP @ SY1499 @ SY1498 @ ( hAPP @ SV82 @ ( fun @ SY1499 @ SY1498 ) @ SY1500 @ SY1502 ) @ ( hAPP @ SV82 @ SY1499 @ SY1501 @ SY1502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(539,plain,
! [SV83: $i] :
( ( ( ( ti @ bool @ SV83 )
= fTrue )
| ( ( ti @ bool @ SV83 )
= fFalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(540,plain,
! [SV84: $i] :
( ( ! [SY1503: $i,SY1504: $i] :
( ~ ( hBOOL @ ( hAPP @ SV84 @ bool @ ( hAPP @ SV84 @ ( fun @ SV84 @ bool ) @ ( fequal @ SV84 ) @ SY1503 ) @ SY1504 ) )
| ( ( ti @ SV84 @ SY1503 )
= ( ti @ SV84 @ SY1504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(541,plain,
! [SV85: $i] :
( ( ! [SY1505: $i,SY1506: $i] :
( ( ( ti @ SV85 @ SY1505 )
!= ( ti @ SV85 @ SY1506 ) )
| ( hBOOL @ ( hAPP @ SV85 @ bool @ ( hAPP @ SV85 @ ( fun @ SV85 @ bool ) @ ( fequal @ SV85 ) @ SY1505 ) @ SY1506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(542,plain,
( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(543,plain,
! [SV86: $i] :
( ( ! [SY1507: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SY1508: $i,SY1509: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1509 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1507 )
= ( ti @ arrow_1212486748le_alt @ SY1509 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1507 )
!= ( ti @ arrow_1212486748le_alt @ SY1509 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1508 ) @ SY1509 ) ) ) )
| ~ ! [SY1510: $i,SY1511: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1511 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1507 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1507 )
!= ( ti @ arrow_1212486748le_alt @ SY1511 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1510 ) @ SY1511 ) ) ) ) )
| ~ ~ ( ~ ! [SY1512: $i,SY1513: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1513 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1507 )
= ( ti @ arrow_1212486748le_alt @ SY1513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ SY1512 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1512 ) @ SY1513 ) ) ) )
| ~ ! [SY1514: $i,SY1515: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1515 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1507 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ SY1514 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1514 ) @ SY1515 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1516: $i,SY1517: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1516 ) @ SY1517 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1517 ) ) )
| ~ ! [SY1518: $i,SY1519: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1518 ) @ SY1519 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1507 )
!= ( ti @ arrow_1212486748le_alt @ SY1519 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1507 ) ) ) )
| ~ ! [SY1520: $i,SY1521: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1520 ) @ SY1521 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1507 )
= ( ti @ arrow_1212486748le_alt @ SY1521 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SY1507 ) ) @ SY1520 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(544,plain,
! [SV87: $i] :
( ( ! [SY1522: $i,SY1523: $i,SY1524: $i] :
~ ( ~ ! [SY1525: $i,SY1526: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1525 )
= ( ti @ arrow_1212486748le_alt @ SY1526 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1523 )
= ( ti @ arrow_1212486748le_alt @ SY1524 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1522 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1525 ) @ SY1526 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1522 @ ( sK30_I @ SY1526 @ SY1525 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1523 ) @ SY1524 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY1526 @ SY1525 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1525 ) @ SY1526 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1522 @ ( sK30_I @ SY1526 @ SY1525 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1523 ) @ SY1524 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY1526 @ SY1525 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1525 ) @ SY1526 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1522 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1523 ) @ SY1524 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
| ~ ! [SY1527: $i,SY1528: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1527 )
= ( ti @ arrow_1212486748le_alt @ SY1528 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1523 )
= ( ti @ arrow_1212486748le_alt @ SY1524 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1522 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1527 ) @ SY1528 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1522 @ ( sK29_I @ SY1528 @ SY1527 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1523 ) @ SY1524 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY1528 @ SY1527 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1527 ) @ SY1528 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1522 @ ( sK29_I @ SY1528 @ SY1527 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1523 ) @ SY1524 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY1528 @ SY1527 @ SY1524 @ SY1523 @ SY1522 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1523 ) @ SY1524 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1527 ) @ SY1528 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1522 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(545,plain,
! [SV88: $i] :
( ( ! [SY1529: $i,SY1530: $i,SY1531: $i] :
~ ( ~ ! [SY1532: $i] :
( ! [SY1533: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SY1529 @ SV88 ) @ ( hAPP @ SY1529 @ ( fun @ SV88 @ ( product_prod @ SY1529 @ SV88 ) ) @ ( product_Pair @ SY1529 @ SV88 ) @ SY1530 ) @ SY1531 )
!= ( hAPP @ SV88 @ ( product_prod @ SY1529 @ SV88 ) @ ( hAPP @ SY1529 @ ( fun @ SV88 @ ( product_prod @ SY1529 @ SV88 ) ) @ ( product_Pair @ SY1529 @ SV88 ) @ SY1532 ) @ SY1533 ) )
| ( ( ti @ SY1529 @ SY1530 )
= ( ti @ SY1529 @ SY1532 ) ) )
| ~ ! [SY1534: $i,SY1535: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SY1529 @ SV88 ) @ ( hAPP @ SY1529 @ ( fun @ SV88 @ ( product_prod @ SY1529 @ SV88 ) ) @ ( product_Pair @ SY1529 @ SV88 ) @ SY1530 ) @ SY1531 )
!= ( hAPP @ SV88 @ ( product_prod @ SY1529 @ SV88 ) @ ( hAPP @ SY1529 @ ( fun @ SV88 @ ( product_prod @ SY1529 @ SV88 ) ) @ ( product_Pair @ SY1529 @ SV88 ) @ SY1534 ) @ SY1535 ) )
| ( ( ti @ SV88 @ SY1531 )
= ( ti @ SV88 @ SY1535 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(546,plain,
! [SV89: $i] :
( ( ! [SY1536: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SY1537: $i,SY1538: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1536 )
= ( ti @ arrow_1212486748le_alt @ SY1538 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1538 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1538 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1537 ) @ SY1538 ) ) ) )
| ~ ! [SY1539: $i,SY1540: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1536 )
= ( ti @ arrow_1212486748le_alt @ SY1540 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1536 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1540 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1539 ) @ SY1540 ) ) ) ) )
| ~ ~ ( ~ ! [SY1541: $i,SY1542: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1536 )
= ( ti @ arrow_1212486748le_alt @ SY1542 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ SY1541 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1541 ) @ SY1542 ) ) ) )
| ~ ! [SY1543: $i,SY1544: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1536 )
= ( ti @ arrow_1212486748le_alt @ SY1544 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1536 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ SY1543 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1543 ) @ SY1544 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1545: $i,SY1546: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1545 ) @ SY1546 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1536 )
!= ( ti @ arrow_1212486748le_alt @ SY1546 ) ) )
| ~ ! [SY1547: $i,SY1548: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1547 ) @ SY1548 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1548 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1536 ) ) ) )
| ~ ! [SY1549: $i,SY1550: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1549 ) @ SY1550 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1550 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SY1536 ) ) @ SY1549 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(547,plain,
! [SV90: $i] :
( ( ~ ( linorder @ SV90 )
| ~ ( ~ ! [SY1551: $i,SY1552: $i] :
( ( ( ti @ SV90 @ SY1551 )
= ( ti @ SV90 @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1551 ) @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1552 ) @ SY1551 ) ) )
| ~ ~ ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) )
| ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(548,plain,
! [SV91: $i] :
( ( ~ ( ~ ! [SY1557: $i,SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1558 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1557 ) @ SV91 ) ) @ SY1558 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1557 ) ) @ SY1558 ) ) )
| ~ ! [SY1559: $i,SY1560: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1560 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1559 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1559 ) ) @ SY1560 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1559 ) @ SV91 ) ) @ SY1560 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(549,plain,
! [SV92: $i] :
( ( ~ ( top @ SV92 )
| ~ ( ~ ! [SY1561: $i] :
( ( ( ti @ SV92 @ SY1561 )
= ( top_top @ SV92 ) )
| ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1561 ) @ ( top_top @ SV92 ) ) ) )
| ~ ! [SY1562: $i] :
( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1562 ) @ ( top_top @ SV92 ) ) )
| ( ( ti @ SV92 @ SY1562 )
!= ( top_top @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(550,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(551,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ! [SX1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK15_X_1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK14_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(552,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(553,plain,
! [SV93: $i] :
( ( ~ ( linorder @ SV93 )
| ~ ( ~ ! [SY1563: $i,SY1564: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1563 ) @ SY1564 ) )
| ( ( ti @ SV93 @ SY1564 )
!= ( ti @ SV93 @ SY1563 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1564 ) @ SY1563 ) ) )
| ~ ! [SY1565: $i,SY1566: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1565 ) @ SY1566 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1566 ) @ SY1565 ) )
| ( ( ti @ SV93 @ SY1566 )
= ( ti @ SV93 @ SY1565 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(554,plain,
! [SV94: $i] :
( ( ! [SY1567: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1567 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SY1567 @ SV94 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SY1567 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SY1567 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SY1567 @ SV94 ) ) @ ( sK5_SY1308 @ SY1567 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SY1567 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SY1567 @ SV94 ) ) @ ( sK5_SY1308 @ SY1567 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1567 @ ( sK3_X_1 @ SY1567 @ SV94 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SY1567 ) @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(555,plain,
! [SV95: $i] :
( ( ! [SY1568: $i,SY1569: $i,SY1570: $i] :
~ ( ~ ! [SY1571: $i,SY1572: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1571 )
= ( ti @ arrow_1212486748le_alt @ SY1572 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1569 )
= ( ti @ arrow_1212486748le_alt @ SY1570 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1571 )
= ( ti @ arrow_1212486748le_alt @ SY1570 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1572 )
= ( ti @ arrow_1212486748le_alt @ SY1569 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1568 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1571 ) @ SY1572 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1568 @ ( sK35_I @ SY1572 @ SY1571 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1569 ) @ SY1570 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY1572 @ SY1571 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1571 ) @ SY1572 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1568 @ ( sK35_I @ SY1572 @ SY1571 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1569 ) @ SY1570 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY1572 @ SY1571 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1571 ) @ SY1572 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1568 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1569 ) @ SY1570 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
| ~ ! [SY1573: $i,SY1574: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1573 )
= ( ti @ arrow_1212486748le_alt @ SY1574 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1569 )
= ( ti @ arrow_1212486748le_alt @ SY1570 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1573 )
= ( ti @ arrow_1212486748le_alt @ SY1570 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1574 )
= ( ti @ arrow_1212486748le_alt @ SY1569 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1568 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1573 ) @ SY1574 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1568 @ ( sK34_I @ SY1574 @ SY1573 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1569 ) @ SY1570 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY1574 @ SY1573 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1573 ) @ SY1574 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1568 @ ( sK34_I @ SY1574 @ SY1573 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1569 ) @ SY1570 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY1574 @ SY1573 @ SY1570 @ SY1569 @ SY1568 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1569 ) @ SY1570 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1573 ) @ SY1574 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1568 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(556,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(557,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(558,plain,
! [SV96: $i] :
( ( ! [SY1575: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SY1575 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ SY1575 @ SV96 ) ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV96 ) @ SY1575 ) ) @ ( sK2_X_1 @ SY1575 @ SV96 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(559,plain,
! [SV97: $i] :
( ( ~ ( linorder @ SV97 )
| ~ ( ~ ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) )
| ~ ! [SY1580: $i,SY1581: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1580 ) @ SY1581 ) )
| ( ( ti @ SV97 @ SY1580 )
= ( ti @ SV97 @ SY1581 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1581 ) @ SY1580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(560,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(561,plain,
! [SV98: $i] :
( ( ! [SY1582: $i,SY1583: $i] :
~ ( ~ ! [SY1584: $i,SY1585: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SY1582 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SY1582 ) @ SY1585 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SY1582 @ SY1585 @ SY1583 )
!= ( hAPP @ SV98 @ SY1582 @ SY1585 @ SY1584 ) )
| ( ( ti @ SV98 @ SY1583 )
= ( ti @ SV98 @ SY1584 ) ) )
| ~ ! [SY1586: $i,SY1587: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SY1582 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SY1582 ) @ SY1587 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SY1583 )
!= ( ti @ SV98 @ SY1586 ) )
| ( ( hAPP @ SV98 @ SY1582 @ SY1587 @ SY1583 )
= ( hAPP @ SV98 @ SY1582 @ SY1587 @ SY1586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(562,plain,
! [SV99: $i] :
( ( ! [SY1588: $i,SY1589: $i] :
~ ( ~ ! [SY1590: $i,SY1591: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1590 )
= ( ti @ arrow_1212486748le_alt @ SY1591 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1591 )
= ( ti @ arrow_1212486748le_alt @ SY1589 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1590 )
= ( ti @ arrow_1212486748le_alt @ SY1589 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1588 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1590 ) @ SY1591 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1588 @ ( sK32_I @ SY1591 @ SY1590 @ SY1589 @ SY1588 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1591 ) @ SY1589 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1591 @ SY1590 @ SY1589 @ SY1588 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1590 ) @ SY1591 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1588 @ ( sK32_I @ SY1591 @ SY1590 @ SY1589 @ SY1588 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1591 ) @ SY1589 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1591 @ SY1590 @ SY1589 @ SY1588 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1590 ) @ SY1591 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1588 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1591 ) @ SY1589 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
| ~ ! [SY1592: $i,SY1593: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1592 )
= ( ti @ arrow_1212486748le_alt @ SY1593 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1593 )
= ( ti @ arrow_1212486748le_alt @ SY1589 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1592 )
= ( ti @ arrow_1212486748le_alt @ SY1589 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1588 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1592 ) @ SY1593 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1588 @ ( sK31_I @ SY1593 @ SY1592 @ SY1589 @ SY1588 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1593 ) @ SY1589 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1593 @ SY1592 @ SY1589 @ SY1588 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1592 ) @ SY1593 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1588 @ ( sK31_I @ SY1593 @ SY1592 @ SY1589 @ SY1588 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1593 ) @ SY1589 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1593 @ SY1592 @ SY1589 @ SY1588 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1593 ) @ SY1589 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1592 ) @ SY1593 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1588 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(563,plain,
! [SV100: $i] :
( ( ~ ( ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1594 ) @ SY1595 ) )
| ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1595 @ SY1594 ) ) )
| ~ ! [SY1596: $i,SY1597: $i] :
( ~ ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1597 @ SY1596 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1596 ) @ SY1597 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(564,plain,
! [SV101: $i] :
( ( ~ ( ~ ! [SY1598: $i,SY1599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( sK26_X1 @ SY1599 @ SY1598 @ SV101 ) ) )
| ! [SY1600: $i,SY1601: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( hAPP @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) @ ( hAPP @ SV101 @ ( fun @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) ) @ ( product_Pair @ SV101 @ SY1598 ) @ SY1600 ) @ SY1601 ) ) ) )
| ~ ! [SY1602: $i,SY1603: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ ( hAPP @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) @ ( hAPP @ SV101 @ ( fun @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) ) @ ( product_Pair @ SV101 @ SY1602 ) @ ( sK24_A_2 @ SY1603 @ SY1602 @ SV101 ) ) @ ( sK25_SY1332 @ SY1603 @ SY1602 @ SV101 ) ) ) )
| ! [SY1604: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ SY1604 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(565,plain,
! [SV102: $i] :
( ( ! [SY1605: $i,SY1606: $i,SY1607: $i] :
~ ( ~ ! [SY1608: $i,SY1609: $i] :
( ( ( ti @ SY1605 @ SY1606 )
!= ( ti @ SY1605 @ SY1608 ) )
| ( ( ti @ SV102 @ SY1607 )
!= ( ti @ SV102 @ SY1609 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SY1605 @ SV102 ) @ ( hAPP @ SY1605 @ ( fun @ SV102 @ ( product_prod @ SY1605 @ SV102 ) ) @ ( product_Pair @ SY1605 @ SV102 ) @ SY1606 ) @ SY1607 )
= ( hAPP @ SV102 @ ( product_prod @ SY1605 @ SV102 ) @ ( hAPP @ SY1605 @ ( fun @ SV102 @ ( product_prod @ SY1605 @ SV102 ) ) @ ( product_Pair @ SY1605 @ SV102 ) @ SY1608 ) @ SY1609 ) ) )
| ~ ~ ( ~ ! [SY1610: $i] :
( ! [SY1611: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SY1605 @ SV102 ) @ ( hAPP @ SY1605 @ ( fun @ SV102 @ ( product_prod @ SY1605 @ SV102 ) ) @ ( product_Pair @ SY1605 @ SV102 ) @ SY1606 ) @ SY1607 )
!= ( hAPP @ SV102 @ ( product_prod @ SY1605 @ SV102 ) @ ( hAPP @ SY1605 @ ( fun @ SV102 @ ( product_prod @ SY1605 @ SV102 ) ) @ ( product_Pair @ SY1605 @ SV102 ) @ SY1610 ) @ SY1611 ) )
| ( ( ti @ SY1605 @ SY1606 )
= ( ti @ SY1605 @ SY1610 ) ) )
| ~ ! [SY1612: $i,SY1613: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SY1605 @ SV102 ) @ ( hAPP @ SY1605 @ ( fun @ SV102 @ ( product_prod @ SY1605 @ SV102 ) ) @ ( product_Pair @ SY1605 @ SV102 ) @ SY1606 ) @ SY1607 )
!= ( hAPP @ SV102 @ ( product_prod @ SY1605 @ SV102 ) @ ( hAPP @ SY1605 @ ( fun @ SV102 @ ( product_prod @ SY1605 @ SV102 ) ) @ ( product_Pair @ SY1605 @ SV102 ) @ SY1612 ) @ SY1613 ) )
| ( ( ti @ SV102 @ SY1607 )
= ( ti @ SV102 @ SY1613 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(566,plain,
! [SV103: $i] :
( ( ! [SY1614: $i,SY1615: $i,SY1616: $i] :
~ ( ~ ! [SY1617: $i,SY1618: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SY1614 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SY1614 ) @ SY1617 ) @ SY1618 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1616 ) @ SY1618 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1615 ) @ SY1618 ) )
| ( ( hAPP @ SV103 @ SY1614 @ SY1617 @ SY1616 )
!= ( hAPP @ SV103 @ SY1614 @ SY1617 @ SY1615 ) )
| ( ( ti @ SV103 @ SY1616 )
= ( ti @ SV103 @ SY1615 ) ) )
| ~ ! [SY1619: $i,SY1620: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SY1614 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SY1614 ) @ SY1619 ) @ SY1620 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1616 ) @ SY1620 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1615 ) @ SY1620 ) )
| ( ( ti @ SV103 @ SY1616 )
!= ( ti @ SV103 @ SY1615 ) )
| ( ( hAPP @ SV103 @ SY1614 @ SY1619 @ SY1616 )
= ( hAPP @ SV103 @ SY1614 @ SY1619 @ SY1615 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(567,plain,
! [SV104: $i] :
( ( ! [SY1621: $i,SY1622: $i] :
( ~ ( ( ( hAPP @ SV104 @ SY1621 @ SY1622 @ ( sK7_X_1 @ SY1622 @ SY1621 @ SV104 ) )
!= ( hAPP @ SV104 @ SY1621 @ SY1622 @ ( sK8_SY1309 @ SY1622 @ SY1621 @ SV104 ) ) )
| ~ ( ( ( ti @ SV104 @ ( sK7_X_1 @ SY1622 @ SY1621 @ SV104 ) )
!= ( ti @ SV104 @ ( sK8_SY1309 @ SY1622 @ SY1621 @ SV104 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SY1621 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SY1621 ) @ SY1622 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(568,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(569,plain,
! [SV105: $i] :
( ( ! [SY1623: $i] :
~ ( ~ ! [SY1624: $i,SY1625: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ ( sK12_X_1 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) @ ( sK13_SY1311 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) ) @ SY1625 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ ( sK12_X_1 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) @ ( sK13_SY1311 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) ) @ SY1624 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ ( sK12_X_1 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) @ ( sK13_SY1311 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) ) @ SY1625 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ ( sK12_X_1 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) @ ( sK13_SY1311 @ SY1625 @ SY1624 @ SY1623 @ SV105 ) ) ) @ SY1624 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ SY1625 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ SY1624 ) ) )
| ~ ! [SY1626: $i,SY1627: $i] :
( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ SY1627 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ SY1626 ) )
| ~ ( ~ ! [SY1628: $i,SY1629: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ SY1628 ) @ SY1629 ) ) @ SY1627 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ SY1628 ) @ SY1629 ) ) @ SY1626 ) ) )
| ~ ! [SY1630: $i,SY1631: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ SY1630 ) @ SY1631 ) ) @ SY1626 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SY1623 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SY1623 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SY1623 ) ) @ ( hAPP @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) @ ( hAPP @ SV105 @ ( fun @ SY1623 @ ( product_prod @ SV105 @ SY1623 ) ) @ ( product_Pair @ SV105 @ SY1623 ) @ SY1630 ) @ SY1631 ) ) @ SY1627 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(570,plain,
! [SV106: $i] :
( ( ! [SY1632: $i] :
~ ( ~ ! [SY1633: $i,SY1634: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SY1634 @ SY1633 @ SY1632 @ SV106 ) ) @ SY1634 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SY1634 @ SY1633 @ SY1632 @ SV106 ) ) @ SY1634 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SY1632 @ SY1633 @ ( sK10_X_1 @ SY1634 @ SY1633 @ SY1632 @ SV106 ) )
!= ( hAPP @ SV106 @ SY1632 @ SY1633 @ ( sK11_SY1310 @ SY1634 @ SY1633 @ SY1632 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SY1634 @ SY1633 @ SY1632 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SY1634 @ SY1633 @ SY1632 @ SV106 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SY1632 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SY1632 ) @ SY1633 ) @ SY1634 ) ) )
| ~ ! [SY1635: $i,SY1636: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SY1632 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SY1632 ) @ SY1635 ) @ SY1636 ) )
| ! [SY1637: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1637 ) @ SY1636 ) )
| ! [SY1638: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1638 ) @ SY1636 ) )
| ( ( hAPP @ SV106 @ SY1632 @ SY1635 @ SY1637 )
!= ( hAPP @ SV106 @ SY1632 @ SY1635 @ SY1638 ) )
| ( ( ti @ SV106 @ SY1637 )
= ( ti @ SV106 @ SY1638 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(571,plain,
! [SV107: $i] :
( ( ! [SY1639: $i,SY1640: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SY1641: $i,SY1642: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1641 )
= ( ti @ arrow_1212486748le_alt @ SY1642 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1642 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1642 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1641 ) @ SY1642 ) ) ) )
| ~ ! [SY1643: $i,SY1644: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1643 )
= ( ti @ arrow_1212486748le_alt @ SY1644 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1643 ) @ SY1639 ) ) @ SY1640 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1644 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1643 ) @ SY1644 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1645: $i,SY1646: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1645 )
= ( ti @ arrow_1212486748le_alt @ SY1646 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1646 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
= ( ti @ arrow_1212486748le_alt @ SY1646 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
!= ( ti @ arrow_1212486748le_alt @ SY1646 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1645 ) @ SY1646 ) ) ) )
| ~ ! [SY1647: $i,SY1648: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1647 )
= ( ti @ arrow_1212486748le_alt @ SY1648 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1648 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
= ( ti @ arrow_1212486748le_alt @ SY1648 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ SY1640 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1647 ) @ SY1648 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1649: $i,SY1650: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1649 )
= ( ti @ arrow_1212486748le_alt @ SY1650 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1650 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1649 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
!= ( ti @ arrow_1212486748le_alt @ SY1650 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1649 ) @ SY1650 ) ) ) )
| ~ ! [SY1651: $i,SY1652: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1651 )
= ( ti @ arrow_1212486748le_alt @ SY1652 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1652 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1651 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ SY1640 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1651 ) @ SY1652 ) ) ) ) )
| ~ ~ ( ~ ! [SY1653: $i,SY1654: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1653 )
= ( ti @ arrow_1212486748le_alt @ SY1654 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1654 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1653 ) ) @ SY1640 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
!= ( ti @ arrow_1212486748le_alt @ SY1654 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1653 ) @ SY1654 ) ) ) )
| ~ ! [SY1655: $i,SY1656: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1655 )
= ( ti @ arrow_1212486748le_alt @ SY1656 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1656 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1655 ) ) @ SY1640 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ SY1640 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1655 ) @ SY1656 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1657: $i,SY1658: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1657 )
= ( ti @ arrow_1212486748le_alt @ SY1658 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1657 ) @ SY1639 ) ) @ SY1640 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
= ( ti @ arrow_1212486748le_alt @ SY1658 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
!= ( ti @ arrow_1212486748le_alt @ SY1658 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1657 ) @ SY1658 ) ) ) )
| ~ ! [SY1659: $i,SY1660: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1659 )
= ( ti @ arrow_1212486748le_alt @ SY1660 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1659 ) @ SY1639 ) ) @ SY1640 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
= ( ti @ arrow_1212486748le_alt @ SY1660 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ SY1640 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1659 ) @ SY1660 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1661: $i,SY1662: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1661 )
= ( ti @ arrow_1212486748le_alt @ SY1662 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1661 ) @ SY1639 ) ) @ SY1640 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1661 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
!= ( ti @ arrow_1212486748le_alt @ SY1662 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1661 ) @ SY1662 ) ) ) )
| ~ ! [SY1663: $i,SY1664: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1663 )
= ( ti @ arrow_1212486748le_alt @ SY1664 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1663 ) @ SY1639 ) ) @ SY1640 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1663 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ SY1640 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1663 ) @ SY1664 ) ) ) ) )
| ~ ~ ( ~ ! [SY1665: $i,SY1666: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1665 )
= ( ti @ arrow_1212486748le_alt @ SY1666 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1665 ) @ SY1639 ) ) @ SY1640 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1665 ) ) @ SY1640 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
!= ( ti @ arrow_1212486748le_alt @ SY1666 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1665 ) @ SY1666 ) ) ) )
| ~ ! [SY1667: $i,SY1668: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1667 )
= ( ti @ arrow_1212486748le_alt @ SY1668 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1639 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1667 ) @ SY1639 ) ) @ SY1640 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1667 ) ) @ SY1640 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ SY1640 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1667 ) @ SY1668 ) ) ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1669: $i,SY1670: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1669 )
= ( ti @ arrow_1212486748le_alt @ SY1670 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1669 ) @ SY1670 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1639 ) ) )
| ~ ! [SY1671: $i,SY1672: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1671 )
= ( ti @ arrow_1212486748le_alt @ SY1672 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1671 ) @ SY1672 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1672 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1671 ) @ SY1639 ) ) @ SY1640 ) ) ) )
| ~ ~ ( ~ ! [SY1673: $i,SY1674: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1673 )
= ( ti @ arrow_1212486748le_alt @ SY1674 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1673 ) @ SY1674 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1674 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
!= ( ti @ arrow_1212486748le_alt @ SY1674 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1673 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1673 ) ) @ SY1640 ) ) )
| ~ ! [SY1675: $i,SY1676: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1675 )
= ( ti @ arrow_1212486748le_alt @ SY1676 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1640 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1640 ) @ SY1675 ) @ SY1676 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1676 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1639 )
= ( ti @ arrow_1212486748le_alt @ SY1676 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1639 ) ) @ SY1640 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(572,plain,
! [SV108: $i] :
( ( ! [SY1677: $i] :
~ ( ~ ! [SY1678: $i,SY1679: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1678 )
= ( ti @ arrow_1212486748le_alt @ SY1679 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1677 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1678 ) @ SY1679 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1677 @ ( sK28_I @ SY1679 @ SY1678 @ SY1677 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1679 ) @ SY1678 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1679 @ SY1678 @ SY1677 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1678 ) @ SY1679 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1677 @ ( sK28_I @ SY1679 @ SY1678 @ SY1677 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1679 ) @ SY1678 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1679 @ SY1678 @ SY1677 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1678 ) @ SY1679 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1677 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1679 ) @ SY1678 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
| ~ ! [SY1680: $i,SY1681: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1680 )
= ( ti @ arrow_1212486748le_alt @ SY1681 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1677 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1680 ) @ SY1681 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1677 @ ( sK27_I @ SY1681 @ SY1680 @ SY1677 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1681 ) @ SY1680 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1681 @ SY1680 @ SY1677 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1680 ) @ SY1681 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1677 @ ( sK27_I @ SY1681 @ SY1680 @ SY1677 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1681 ) @ SY1680 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1681 @ SY1680 @ SY1677 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1681 ) @ SY1680 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1680 ) @ SY1681 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1677 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(573,plain,
! [SV109: $i] :
( ( ! [SY1682: $i,SY1683: $i,SY1684: $i,SY1685: $i,SY1686: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1685 )
= ( ti @ arrow_1212486748le_alt @ SY1686 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1683 )
= ( ti @ arrow_1212486748le_alt @ SY1684 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1685 )
= ( ti @ arrow_1212486748le_alt @ SY1684 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1686 )
= ( ti @ arrow_1212486748le_alt @ SY1683 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY1682 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1685 ) @ SY1686 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1682 @ ( sK33_I @ SY1686 @ SY1685 @ SY1684 @ SY1683 @ SY1682 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1683 ) @ SY1684 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY1686 @ SY1685 @ SY1684 @ SY1683 @ SY1682 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1685 ) @ SY1686 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY1682 @ ( sK33_I @ SY1686 @ SY1685 @ SY1684 @ SY1683 @ SY1682 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1683 ) @ SY1684 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY1686 @ SY1685 @ SY1684 @ SY1683 @ SY1682 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1685 ) @ SY1686 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SY1682 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1683 ) @ SY1684 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(574,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SX1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK1_X_1 @ SX1 @ SX0 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(575,plain,
! [SV110: $i,SV1: $i] :
( ( ! [SY1687: $i] :
( ( ti @ ( fun @ ( fun @ SV1 @ SV110 ) @ ( fun @ ( fun @ SY1687 @ SV1 ) @ ( fun @ SY1687 @ SV110 ) ) ) @ ( combb @ SV1 @ SV110 @ SY1687 ) )
= ( combb @ SV1 @ SV110 @ SY1687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(576,plain,
! [SV111: $i,SV2: $i] :
( ( ! [SY1688: $i] :
( ( ti @ ( fun @ ( fun @ SV2 @ ( fun @ SV111 @ SY1688 ) ) @ ( fun @ SV111 @ ( fun @ SV2 @ SY1688 ) ) ) @ ( combc @ SV2 @ SV111 @ SY1688 ) )
= ( combc @ SV2 @ SV111 @ SY1688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(577,plain,
! [SV112: $i,SV4: $i] :
( ( ( ti @ ( fun @ SV4 @ ( fun @ SV112 @ SV4 ) ) @ ( combk @ SV4 @ SV112 ) )
= ( combk @ SV4 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(578,plain,
! [SV113: $i,SV5: $i] :
( ( ! [SY1689: $i] :
( ( ti @ ( fun @ ( fun @ SV5 @ ( fun @ SV113 @ SY1689 ) ) @ ( fun @ ( fun @ SV5 @ SV113 ) @ ( fun @ SV5 @ SY1689 ) ) ) @ ( combs @ SV5 @ SV113 @ SY1689 ) )
= ( combs @ SV5 @ SV113 @ SY1689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(579,plain,
! [SV114: $i,SV6: $i] :
( ( ( ti @ ( fun @ ( fun @ SV6 @ SV114 ) @ ( fun @ ( fun @ SV6 @ bool ) @ bool ) ) @ ( inj_on @ SV6 @ SV114 ) )
= ( inj_on @ SV6 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(580,plain,
! [SV115: $i,SV7: $i] :
( ( ( ti @ ( fun @ ( fun @ SV7 @ bool ) @ ( fun @ ( fun @ SV7 @ ( fun @ SV115 @ bool ) ) @ ( fun @ ( fun @ SV7 @ SV115 ) @ bool ) ) ) @ ( pi @ SV7 @ SV115 ) )
= ( pi @ SV7 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(581,plain,
! [SV116: $i,SV9: $i] :
( ( ( ti @ ( fun @ ( fun @ SV9 @ bool ) @ ( fun @ ( fun @ SV9 @ SV116 ) @ ( fun @ SV116 @ SV9 ) ) ) @ ( hilbert_inv_into @ SV9 @ SV116 ) )
= ( hilbert_inv_into @ SV9 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(582,plain,
! [SV11: $i] :
( ( ( ~ ( ord @ SV11 ) )
= $true )
| ( ( ( ti @ ( fun @ SV11 @ ( fun @ SV11 @ bool ) ) @ ( ord_less @ SV11 ) )
= ( ord_less @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(583,plain,
! [SV12: $i] :
( ( ( ~ ( top @ SV12 ) )
= $true )
| ( ( ( ti @ SV12 @ ( top_top @ SV12 ) )
= ( top_top @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(584,plain,
! [SV117: $i,SV13: $i] :
( ( ( ti @ ( fun @ SV13 @ ( fun @ SV117 @ ( product_prod @ SV13 @ SV117 ) ) ) @ ( product_Pair @ SV13 @ SV117 ) )
= ( product_Pair @ SV13 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(585,plain,
! [SV118: $i,SV14: $i] :
( ( ! [SY1690: $i] :
( ( ti @ ( fun @ ( fun @ SV14 @ ( fun @ SV118 @ SY1690 ) ) @ ( fun @ ( product_prod @ SV14 @ SV118 ) @ SY1690 ) ) @ ( product_prod_rec @ SV14 @ SV118 @ SY1690 ) )
= ( product_prod_rec @ SV14 @ SV118 @ SY1690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(586,plain,
! [SV119: $i,SV17: $i] :
( ( ! [SY1691: $i,SY1692: $i] :
( ( hAPP @ SV17 @ SV119 @ ( ti @ ( fun @ SV17 @ SV119 ) @ SY1691 ) @ SY1692 )
= ( hAPP @ SV17 @ SV119 @ SY1691 @ SY1692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(587,plain,
! [SV120: $i,SV18: $i] :
( ( ! [SY1693: $i,SY1694: $i] :
( ( hAPP @ SV18 @ SV120 @ SY1693 @ ( ti @ SV18 @ SY1694 ) )
= ( hAPP @ SV18 @ SV120 @ SY1693 @ SY1694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(588,plain,
! [SV121: $i,SV19: $i] :
( ( ! [SY1695: $i,SY1696: $i] :
( ( ti @ SV19 @ ( hAPP @ SV121 @ SV19 @ SY1695 @ SY1696 ) )
= ( hAPP @ SV121 @ SV19 @ SY1695 @ SY1696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(589,plain,
! [SV122: $i,SV21: $i] :
( ( hBOOL @ ( hAPP @ SV21 @ bool @ ( top_top @ ( fun @ SV21 @ bool ) ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(590,plain,
! [SV123: $i,SV22: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ SV22 @ bool ) @ bool @ ( hAPP @ SV22 @ ( fun @ ( fun @ SV22 @ bool ) @ bool ) @ ( member @ SV22 ) @ SV123 ) @ ( top_top @ ( fun @ SV22 @ bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(591,plain,
! [SV124: $i,SV23: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ SV23 @ bool ) @ bool @ ( hAPP @ SV23 @ ( fun @ ( fun @ SV23 @ bool ) @ bool ) @ ( member @ SV23 ) @ SV124 ) @ ( top_top @ ( fun @ SV23 @ bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(592,plain,
! [SV125: $i,SV24: $i] :
( ( ! [SY1697: $i,SY1698: $i,SY1699: $i,SY1700: $i] :
( ( hAPP @ ( product_prod @ SV24 @ SV125 ) @ SY1697 @ ( hAPP @ ( fun @ SV24 @ ( fun @ SV125 @ SY1697 ) ) @ ( fun @ ( product_prod @ SV24 @ SV125 ) @ SY1697 ) @ ( product_prod_rec @ SV24 @ SV125 @ SY1697 ) @ SY1698 ) @ ( hAPP @ SV125 @ ( product_prod @ SV24 @ SV125 ) @ ( hAPP @ SV24 @ ( fun @ SV125 @ ( product_prod @ SV24 @ SV125 ) ) @ ( product_Pair @ SV24 @ SV125 ) @ SY1699 ) @ SY1700 ) )
= ( hAPP @ SV125 @ SY1697 @ ( hAPP @ SV24 @ ( fun @ SV125 @ SY1697 ) @ SY1698 @ SY1699 ) @ SY1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(593,plain,
! [SV25: $i,SV126: $i] :
( ( ~ ( top @ SV126 )
| ! [SY1701: $i] :
( ( hAPP @ SV25 @ SV126 @ ( top_top @ ( fun @ SV25 @ SV126 ) ) @ SY1701 )
= ( top_top @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(594,plain,
! [SV26: $i] :
( ( ( ~ ( top @ SV26 ) )
= $true )
| ( ( ! [SY1365: $i] :
~ ( hBOOL @ ( hAPP @ SV26 @ bool @ ( hAPP @ SV26 @ ( fun @ SV26 @ bool ) @ ( ord_less @ SV26 ) @ ( top_top @ SV26 ) ) @ SY1365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(595,plain,
! [SV27: $i] :
( ( ( ~ ( linorder @ SV27 ) )
= $true )
| ( ( ! [SY1366: $i,SY1367: $i] :
( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SY1366 ) @ SY1367 ) )
| ( ( ti @ SV27 @ SY1366 )
= ( ti @ SV27 @ SY1367 ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SY1367 ) @ SY1366 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(596,plain,
! [SV28: $i] :
( ( ( ~ ( preorder @ SV28 ) )
= $true )
| ( ( ! [SY1368: $i,SY1369: $i] :
( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SY1368 ) @ SY1369 ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SY1369 ) @ SY1368 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(597,plain,
! [SV29: $i] :
( ( ( ~ ( order @ SV29 ) )
= $true )
| ( ( ! [SY1370: $i,SY1371: $i,SY1372: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1371 ) @ SY1372 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1370 ) @ SY1371 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1370 ) @ SY1372 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(598,plain,
! [SV30: $i] :
( ( ( ~ ( preorder @ SV30 ) )
= $true )
| ( ( ! [SY1373: $i,SY1374: $i,SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1374 ) @ SY1375 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1375 ) @ SY1373 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1374 ) @ SY1373 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(599,plain,
! [SV31: $i] :
( ( ( ~ ( order @ SV31 ) )
= $true )
| ( ( ! [SY1376: $i,SY1377: $i,SY1378: $i] :
( ~ ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SY1377 ) @ SY1378 ) )
| ( SY1377 != SY1376 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SY1376 ) @ SY1378 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(600,plain,
! [SV32: $i] :
( ( ( ~ ( ord @ SV32 ) )
= $true )
| ( ( ! [SY1379: $i,SY1380: $i,SY1381: $i] :
( ~ ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY1380 ) @ SY1381 ) )
| ( SY1381 != SY1379 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY1380 ) @ SY1379 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(601,plain,
! [SV33: $i] :
( ( ( ~ ( order @ SV33 ) )
= $true )
| ( ( ! [SY1382: $i,SY1383: $i,SY1384: $i] :
( ( SY1383 != SY1384 )
| ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SY1382 ) @ SY1384 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SY1382 ) @ SY1383 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(602,plain,
! [SV34: $i] :
( ( ( ~ ( ord @ SV34 ) )
= $true )
| ( ( ! [SY1385: $i,SY1386: $i,SY1387: $i] :
( ( SY1386 != SY1387 )
| ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY1387 ) @ SY1385 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY1386 ) @ SY1385 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(603,plain,
! [SV35: $i] :
( ( ( ~ ( order @ SV35 ) )
= $true )
| ( ( ! [SY1388: $i,SY1389: $i] :
( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SY1388 ) @ SY1389 ) )
| ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SY1389 ) @ SY1388 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(604,plain,
! [SV36: $i] :
( ( ( ~ ( preorder @ SV36 ) )
= $true )
| ( ( ! [SY1390: $i,SY1391: $i] :
( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SY1390 ) @ SY1391 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SY1391 ) @ SY1390 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(605,plain,
! [SV37: $i] :
( ( ( ~ ( preorder @ SV37 ) )
= $true )
| ( ( ! [SY1392: $i,SY1393: $i,SY1394: $i] :
( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY1393 ) @ SY1394 ) )
| ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY1394 ) @ SY1393 ) )
| ( hBOOL @ SY1392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(606,plain,
! [SV38: $i] :
( ( ( ~ ( order @ SV38 ) )
= $true )
| ( ( ! [SY1395: $i,SY1396: $i] :
( ~ ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SY1395 ) @ SY1396 ) )
| ( SY1396 != SY1395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(607,plain,
! [SV39: $i] :
( ( ( ~ ( order @ SV39 ) )
= $true )
| ( ( ! [SY1397: $i,SY1398: $i] :
( ~ ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SY1397 ) @ SY1398 ) )
| ( SY1397 != SY1398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(608,plain,
! [SV40: $i] :
( ( ( ~ ( preorder @ SV40 ) )
= $true )
| ( ( ! [SY1399: $i,SY1400: $i] :
( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SY1399 ) @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SY1400 ) @ SY1399 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(609,plain,
! [SV41: $i] :
( ( ( ~ ( preorder @ SV41 ) )
= $true )
| ( ( ! [SY1401: $i,SY1402: $i] :
( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SY1401 ) @ SY1402 ) )
| ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SY1402 ) @ SY1401 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(610,plain,
! [SV42: $i] :
( ( ( ~ ( order @ SV42 ) )
= $true )
| ( ( ! [SY1403: $i,SY1404: $i] :
( ~ ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SY1403 ) @ SY1404 ) )
| ( SY1403 != SY1404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(611,plain,
! [SV43: $i] :
( ( ( ~ ( linorder @ SV43 ) )
= $true )
| ( ( ! [SY1405: $i,SY1406: $i] :
( ( ( ti @ SV43 @ SY1405 )
= ( ti @ SV43 @ SY1406 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SY1405 ) @ SY1406 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SY1406 ) @ SY1405 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(612,plain,
! [SV44: $i] :
( ( ( ~ ( linorder @ SV44 ) )
= $true )
| ( ( ! [SY1407: $i,SY1408: $i] :
( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SY1408 ) @ SY1407 ) )
| ( ( ti @ SV44 @ SY1407 )
= ( ti @ SV44 @ SY1408 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SY1407 ) @ SY1408 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(613,plain,
! [SV45: $i] :
( ( ( ~ ( preorder @ SV45 ) )
= $true )
| ( ( ! [SY1409: $i] :
~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( ord_less @ SV45 ) @ SY1409 ) @ SY1409 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(614,plain,
! [SV127: $i,SV47: $i] :
( ( ! [SY1702: $i,SY1703: $i,SY1704: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SY1704 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
| ( ( hAPP @ SV47 @ SV127 @ SY1704 @ SY1702 )
!= ( ti @ SV127 @ SY1703 ) )
| ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SY1704 ) @ SY1703 )
= ( ti @ SV47 @ SY1702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(615,plain,
! [SV128: $i,SV48: $i] :
( ( ! [SY1705: $i,SY1706: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV48 @ bool ) @ bool @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ ( fun @ SV48 @ bool ) @ bool ) @ ( inj_on @ SV48 @ SV128 ) @ SY1706 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) )
| ( ( hAPP @ SV128 @ SV48 @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) @ ( hAPP @ ( fun @ SV48 @ bool ) @ ( fun @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) ) @ ( hilbert_inv_into @ SV48 @ SV128 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) @ SY1706 ) @ ( hAPP @ SV48 @ SV128 @ SY1706 @ SY1705 ) )
= ( ti @ SV48 @ SY1705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(616,plain,
! [SV49: $i,SV129: $i] :
( ( ! [SY1707: $i,SY1708: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ SY1707 ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ SY1707 ) @ SY1708 ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ ( fun @ SV49 @ SY1707 ) ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ ( fun @ SV49 @ SY1707 ) ) @ ( hAPP @ ( fun @ SV129 @ SY1707 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SY1707 ) ) @ ( hAPP @ ( fun @ SY1707 @ ( fun @ SV49 @ SY1707 ) ) @ ( fun @ ( fun @ SV129 @ SY1707 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SY1707 ) ) ) @ ( combb @ SY1707 @ ( fun @ SV49 @ SY1707 ) @ SV129 ) @ ( combk @ SY1707 @ SV49 ) ) @ SY1708 ) ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(617,plain,
! [SV130: $i,SV50: $i] :
( ( ! [SY1709: $i,SY1710: $i,SY1711: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SY1710 ) @ SY1711 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SY1709 ) @ SY1711 ) )
| ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SY1711 ) @ SY1710 ) @ ( hAPP @ SV50 @ SV130 @ SY1710 @ SY1709 ) )
= ( ti @ SV50 @ SY1709 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(618,plain,
! [SV131: $i,SV51: $i] :
( ( ! [SY1712: $i,SY1713: $i,SY1714: $i,SY1715: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SY1714 ) @ SY1715 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SY1713 ) @ SY1715 ) )
| ( ( hAPP @ SV51 @ SV131 @ SY1714 @ SY1713 )
!= ( ti @ SV131 @ SY1712 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SY1715 ) @ SY1714 ) @ SY1712 )
= ( ti @ SV51 @ SY1713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(619,plain,
! [SV132: $i,SV52: $i] :
( ( ! [SY1716: $i,SY1717: $i,SY1718: $i,SY1719: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SY1718 ) @ SY1719 ) )
| ( ( ti @ SV52 @ SY1716 )
= ( ti @ SV52 @ SY1717 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SY1716 ) @ SY1719 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SY1717 ) @ SY1719 ) )
| ( ( hAPP @ SV52 @ SV132 @ SY1718 @ SY1716 )
!= ( hAPP @ SV52 @ SV132 @ SY1718 @ SY1717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(620,plain,
! [SV133: $i,SV53: $i] :
( ( ! [SY1720: $i,SY1721: $i,SY1722: $i,SY1723: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SY1722 ) @ SY1723 ) )
| ( ( hAPP @ SV53 @ SV133 @ SY1722 @ SY1720 )
!= ( hAPP @ SV53 @ SV133 @ SY1722 @ SY1721 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SY1720 ) @ SY1723 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SY1721 ) @ SY1723 ) )
| ( ( ti @ SV53 @ SY1720 )
= ( ti @ SV53 @ SY1721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(621,plain,
! [SV134: $i,SV54: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ SV54 @ bool ) @ bool @ ( hAPP @ ( fun @ SV54 @ SV54 ) @ ( fun @ ( fun @ SV54 @ bool ) @ bool ) @ ( inj_on @ SV54 @ SV54 ) @ ( combi @ SV54 ) ) @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(622,plain,
! [SV135: $i,SV55: $i] :
( ( ! [SY1724: $i,SY1725: $i,SY1726: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SY1726 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
| ( ( hAPP @ SV55 @ SV135 @ SY1726 @ SY1724 )
!= ( hAPP @ SV55 @ SV135 @ SY1726 @ SY1725 ) )
| ( ( ti @ SV55 @ SY1724 )
= ( ti @ SV55 @ SY1725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(623,plain,
! [SV136: $i,SV56: $i] :
( ( ! [SY1727: $i,SY1728: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SV136 ) @ SY1728 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) )
| ( ( hAPP @ SV56 @ SV136 @ SY1728 @ ( hAPP @ SV136 @ SV56 @ SY1727 @ ( sK9_X_1 @ SY1728 @ SY1727 @ SV136 @ SV56 ) ) )
!= ( ti @ SV136 @ ( sK9_X_1 @ SY1728 @ SY1727 @ SV136 @ SV56 ) ) )
| ( ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SV136 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SY1728 )
= ( ti @ ( fun @ SV136 @ SV56 ) @ SY1727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(624,plain,
! [SV137: $i,SV57: $i] :
( ( ! [SY1729: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1729 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SV137 ) ) @ SY1729 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV137 ) @ SV57 ) ) @ SY1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(625,plain,
! [SV138: $i,SV58: $i] :
( ( ! [SY1730: $i,SY1731: $i] :
( ( ( hAPP @ SV58 @ SV138 @ SY1730 @ ( sK6_X_1 @ SY1731 @ SY1730 @ SV138 @ SV58 ) )
!= ( hAPP @ SV58 @ SV138 @ SY1731 @ ( sK6_X_1 @ SY1731 @ SY1730 @ SV138 @ SV58 ) ) )
| ( ( ti @ ( fun @ SV58 @ SV138 ) @ SY1730 )
= ( ti @ ( fun @ SV58 @ SV138 ) @ SY1731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(626,plain,
! [SV139: $i,SV59: $i] :
( ( ( hAPP @ ( fun @ SV59 @ bool ) @ ( fun @ SV59 @ bool ) @ ( collect @ SV59 ) @ SV139 )
= ( ti @ ( fun @ SV59 @ bool ) @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(627,plain,
! [SV60: $i,SV140: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV140 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV140 ) @ SV60 ) ) @ arrow_638930832le_Lin ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(628,plain,
! [SV61: $i,SV141: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV141 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV141 ) @ SV61 ) ) @ arrow_638930832le_Lin ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(629,plain,
! [SV62: $i,SV142: $i] :
( ( ! [SY1732: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV142 )
= ( ti @ arrow_1212486748le_alt @ SY1732 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV62 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV62 ) @ SV142 ) @ SY1732 ) ) @ arrow_638930832le_Lin ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(630,plain,
! [SV63: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV63 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ arrow_1384031255e_indi ) @ SV63 ) ) @ arrow_1834574746e_Prof ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(631,plain,
! [SV143: $i,SV64: $i] :
( ( ! [SY1733: $i,SY1734: $i,SY1735: $i,SY1736: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SY1734 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SY1735 ) @ SY1736 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SY1734 @ SY1733 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SY1736 @ SY1733 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SY1733 ) @ SY1735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(632,plain,
! [SV144: $i,SV66: $i] :
( ( ! [SY1737: $i,SY1738: $i,SY1739: $i,SY1740: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SY1738 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SY1739 ) @ SY1740 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SY1737 ) @ SY1739 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SY1738 @ SY1737 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SY1740 @ SY1737 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(633,plain,
! [SV145: $i,SV67: $i] :
( ( ! [SY1741: $i,SY1742: $i,SY1743: $i,SY1744: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SY1742 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SY1743 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SY1744 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SY1741 ) @ SY1743 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SY1742 @ SY1741 ) ) @ SY1744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(634,plain,
! [SV146: $i,SV68: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV68 @ SV68 ) @ ( fun @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV68 @ SV68 ) ) @ ( combi @ SV68 ) ) @ ( hAPP @ ( fun @ SV68 @ ( fun @ SV68 @ bool ) ) @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) @ ( hAPP @ ( fun @ SV68 @ bool ) @ ( fun @ ( fun @ SV68 @ ( fun @ SV68 @ bool ) ) @ ( fun @ ( fun @ SV68 @ SV68 ) @ bool ) ) @ ( pi @ SV68 @ SV68 ) @ SV146 ) @ ( hAPP @ ( fun @ SV68 @ bool ) @ ( fun @ SV68 @ ( fun @ SV68 @ bool ) ) @ ( combk @ ( fun @ SV68 @ bool ) @ SV68 ) @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(635,plain,
! [SV147: $i,SV69: $i] :
( ( ! [SY1745: $i] :
( ( hAPP @ ( fun @ SV69 @ ( fun @ SV147 @ bool ) ) @ ( fun @ ( fun @ SV69 @ SV147 ) @ bool ) @ ( hAPP @ ( fun @ SV69 @ bool ) @ ( fun @ ( fun @ SV69 @ ( fun @ SV147 @ bool ) ) @ ( fun @ ( fun @ SV69 @ SV147 ) @ bool ) ) @ ( pi @ SV69 @ SV147 ) @ SY1745 ) @ ( hAPP @ ( fun @ SV147 @ bool ) @ ( fun @ SV69 @ ( fun @ SV147 @ bool ) ) @ ( combk @ ( fun @ SV147 @ bool ) @ SV69 ) @ ( top_top @ ( fun @ SV147 @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ SV69 @ SV147 ) @ bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(636,plain,
! [SV70: $i,SV148: $i] :
( ( ~ ( preorder @ SV148 )
| ( preorder @ ( fun @ SV70 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(637,plain,
! [SV71: $i,SV149: $i] :
( ( ~ ( order @ SV149 )
| ( order @ ( fun @ SV71 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(638,plain,
! [SV72: $i,SV150: $i] :
( ( ~ ( top @ SV150 )
| ( top @ ( fun @ SV72 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(639,plain,
! [SV73: $i,SV151: $i] :
( ( ~ ( ord @ SV151 )
| ( ord @ ( fun @ SV73 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(640,plain,
! [SV152: $i,SV74: $i] :
( ( ( ti @ SV74 @ ( ti @ SV74 @ SV152 ) )
= ( ti @ SV74 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(641,plain,
! [SV153: $i,SV75: $i] :
( ( ! [SY1746: $i] :
( ( hAPP @ SV75 @ SV75 @ ( hAPP @ SV75 @ ( fun @ SV75 @ SV75 ) @ ( hAPP @ bool @ ( fun @ SV75 @ ( fun @ SV75 @ SV75 ) ) @ ( if @ SV75 ) @ fTrue ) @ SV153 ) @ SY1746 )
= ( ti @ SV75 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(642,plain,
! [SV154: $i,SV76: $i] :
( ( ! [SY1747: $i] :
( ( hAPP @ SV76 @ SV76 @ ( hAPP @ SV76 @ ( fun @ SV76 @ SV76 ) @ ( hAPP @ bool @ ( fun @ SV76 @ ( fun @ SV76 @ SV76 ) ) @ ( if @ SV76 ) @ fFalse ) @ SV154 ) @ SY1747 )
= ( ti @ SV76 @ SY1747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(643,plain,
! [SV77: $i] :
( ( ( ( ti @ bool @ SV77 )
= fTrue )
= $true )
| ( ( ( ti @ bool @ SV77 )
= fFalse )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(644,plain,
! [SV155: $i,SV78: $i] :
( ( ! [SY1748: $i,SY1749: $i,SY1750: $i,SY1751: $i] :
( ( hAPP @ SV78 @ SV155 @ ( hAPP @ ( fun @ SV78 @ SY1748 ) @ ( fun @ SV78 @ SV155 ) @ ( hAPP @ ( fun @ SY1748 @ SV155 ) @ ( fun @ ( fun @ SV78 @ SY1748 ) @ ( fun @ SV78 @ SV155 ) ) @ ( combb @ SY1748 @ SV155 @ SV78 ) @ SY1749 ) @ SY1750 ) @ SY1751 )
= ( hAPP @ SY1748 @ SV155 @ SY1749 @ ( hAPP @ SV78 @ SY1748 @ SY1750 @ SY1751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(645,plain,
! [SV156: $i,SV79: $i] :
( ( ! [SY1752: $i,SY1753: $i,SY1754: $i,SY1755: $i] :
( ( hAPP @ SV79 @ SV156 @ ( hAPP @ SY1752 @ ( fun @ SV79 @ SV156 ) @ ( hAPP @ ( fun @ SV79 @ ( fun @ SY1752 @ SV156 ) ) @ ( fun @ SY1752 @ ( fun @ SV79 @ SV156 ) ) @ ( combc @ SV79 @ SY1752 @ SV156 ) @ SY1753 ) @ SY1754 ) @ SY1755 )
= ( hAPP @ SY1752 @ SV156 @ ( hAPP @ SV79 @ ( fun @ SY1752 @ SV156 ) @ SY1753 @ SY1755 ) @ SY1754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(646,plain,
! [SV157: $i,SV80: $i] :
( ( ( hAPP @ SV80 @ SV80 @ ( combi @ SV80 ) @ SV157 )
= ( ti @ SV80 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(647,plain,
! [SV158: $i,SV81: $i] :
( ( ! [SY1756: $i,SY1757: $i] :
( ( hAPP @ SV81 @ SV158 @ ( hAPP @ SV158 @ ( fun @ SV81 @ SV158 ) @ ( combk @ SV158 @ SV81 ) @ SY1756 ) @ SY1757 )
= ( ti @ SV158 @ SY1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(648,plain,
! [SV159: $i,SV82: $i] :
( ( ! [SY1758: $i,SY1759: $i,SY1760: $i,SY1761: $i] :
( ( hAPP @ SV82 @ SV159 @ ( hAPP @ ( fun @ SV82 @ SY1758 ) @ ( fun @ SV82 @ SV159 ) @ ( hAPP @ ( fun @ SV82 @ ( fun @ SY1758 @ SV159 ) ) @ ( fun @ ( fun @ SV82 @ SY1758 ) @ ( fun @ SV82 @ SV159 ) ) @ ( combs @ SV82 @ SY1758 @ SV159 ) @ SY1759 ) @ SY1760 ) @ SY1761 )
= ( hAPP @ SY1758 @ SV159 @ ( hAPP @ SV82 @ ( fun @ SY1758 @ SV159 ) @ SY1759 @ SY1761 ) @ ( hAPP @ SV82 @ SY1758 @ SY1760 @ SY1761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(649,plain,
! [SV83: $i] :
( ( ( ( ti @ bool @ SV83 )
= fTrue )
= $true )
| ( ( ( ti @ bool @ SV83 )
= fFalse )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(650,plain,
! [SV160: $i,SV84: $i] :
( ( ! [SY1762: $i] :
( ~ ( hBOOL @ ( hAPP @ SV84 @ bool @ ( hAPP @ SV84 @ ( fun @ SV84 @ bool ) @ ( fequal @ SV84 ) @ SV160 ) @ SY1762 ) )
| ( ( ti @ SV84 @ SV160 )
= ( ti @ SV84 @ SY1762 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(651,plain,
! [SV161: $i,SV85: $i] :
( ( ! [SY1763: $i] :
( ( ( ti @ SV85 @ SV161 )
!= ( ti @ SV85 @ SY1763 ) )
| ( hBOOL @ ( hAPP @ SV85 @ bool @ ( hAPP @ SV85 @ ( fun @ SV85 @ bool ) @ ( fequal @ SV85 ) @ SV161 ) @ SY1763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(652,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
| ~ ~ ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
| ~ ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1776 ) @ SY1777 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1777 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1776 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(653,plain,
! [SV87: $i,SV163: $i] :
( ( ! [SY1778: $i,SY1779: $i] :
~ ( ~ ! [SY1780: $i,SY1781: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1780 )
= ( ti @ arrow_1212486748le_alt @ SY1781 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1778 )
= ( ti @ arrow_1212486748le_alt @ SY1779 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1780 ) @ SY1781 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY1781 @ SY1780 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1778 ) @ SY1779 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY1781 @ SY1780 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1780 ) @ SY1781 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY1781 @ SY1780 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1778 ) @ SY1779 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY1781 @ SY1780 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1780 ) @ SY1781 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1778 ) @ SY1779 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
| ~ ! [SY1782: $i,SY1783: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1782 )
= ( ti @ arrow_1212486748le_alt @ SY1783 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1778 )
= ( ti @ arrow_1212486748le_alt @ SY1779 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1782 ) @ SY1783 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY1783 @ SY1782 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1778 ) @ SY1779 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY1783 @ SY1782 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1782 ) @ SY1783 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY1783 @ SY1782 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1778 ) @ SY1779 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY1783 @ SY1782 @ SY1779 @ SY1778 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1778 ) @ SY1779 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1782 ) @ SY1783 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(654,plain,
! [SV164: $i,SV88: $i] :
( ( ! [SY1784: $i,SY1785: $i] :
~ ( ~ ! [SY1786: $i] :
( ! [SY1787: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY1784 ) @ SY1785 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY1786 ) @ SY1787 ) )
| ( ( ti @ SV164 @ SY1784 )
= ( ti @ SV164 @ SY1786 ) ) )
| ~ ! [SY1788: $i,SY1789: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY1784 ) @ SY1785 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY1788 ) @ SY1789 ) )
| ( ( ti @ SV88 @ SY1785 )
= ( ti @ SV88 @ SY1789 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(655,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
| ~ ~ ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
| ~ ! [SY1802: $i,SY1803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1802 ) @ SY1803 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1803 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1802 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(656,plain,
! [SV90: $i] :
( ( ( ~ ( linorder @ SV90 ) )
= $true )
| ( ( ~ ( ~ ! [SY1551: $i,SY1552: $i] :
( ( ( ti @ SV90 @ SY1551 )
= ( ti @ SV90 @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1551 ) @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1552 ) @ SY1551 ) ) )
| ~ ~ ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) )
| ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(657,plain,
! [SV91: $i] :
( ( ~ ! [SY1557: $i,SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1558 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1557 ) @ SV91 ) ) @ SY1558 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1557 ) ) @ SY1558 ) ) )
| ~ ! [SY1559: $i,SY1560: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1560 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1559 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1559 ) ) @ SY1560 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1559 ) @ SV91 ) ) @ SY1560 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(658,plain,
! [SV92: $i] :
( ( ( ~ ( top @ SV92 ) )
= $true )
| ( ( ~ ( ~ ! [SY1561: $i] :
( ( ( ti @ SV92 @ SY1561 )
= ( top_top @ SV92 ) )
| ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1561 ) @ ( top_top @ SV92 ) ) ) )
| ~ ! [SY1562: $i] :
( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1562 ) @ ( top_top @ SV92 ) ) )
| ( ( ti @ SV92 @ SY1562 )
!= ( top_top @ SV92 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(659,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(660,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(661,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ! [SX1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK15_X_1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(662,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK14_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(663,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(664,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(665,plain,
! [SV93: $i] :
( ( ( ~ ( linorder @ SV93 ) )
= $true )
| ( ( ~ ( ~ ! [SY1563: $i,SY1564: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1563 ) @ SY1564 ) )
| ( ( ti @ SV93 @ SY1564 )
!= ( ti @ SV93 @ SY1563 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1564 ) @ SY1563 ) ) )
| ~ ! [SY1565: $i,SY1566: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1565 ) @ SY1566 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1566 ) @ SY1565 ) )
| ( ( ti @ SV93 @ SY1566 )
= ( ti @ SV93 @ SY1565 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(666,plain,
! [SV94: $i,SV166: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SV166 @ SV94 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(667,plain,
! [SV95: $i,SV167: $i] :
( ( ! [SY1804: $i,SY1805: $i] :
~ ( ~ ! [SY1806: $i,SY1807: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1806 )
= ( ti @ arrow_1212486748le_alt @ SY1807 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1804 )
= ( ti @ arrow_1212486748le_alt @ SY1805 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1806 )
= ( ti @ arrow_1212486748le_alt @ SY1805 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1807 )
= ( ti @ arrow_1212486748le_alt @ SY1804 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1806 ) @ SY1807 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY1807 @ SY1806 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1804 ) @ SY1805 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY1807 @ SY1806 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1806 ) @ SY1807 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY1807 @ SY1806 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1804 ) @ SY1805 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY1807 @ SY1806 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1806 ) @ SY1807 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1804 ) @ SY1805 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
| ~ ! [SY1808: $i,SY1809: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1808 )
= ( ti @ arrow_1212486748le_alt @ SY1809 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1804 )
= ( ti @ arrow_1212486748le_alt @ SY1805 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1808 )
= ( ti @ arrow_1212486748le_alt @ SY1805 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1809 )
= ( ti @ arrow_1212486748le_alt @ SY1804 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1808 ) @ SY1809 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY1809 @ SY1808 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1804 ) @ SY1805 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY1809 @ SY1808 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1808 ) @ SY1809 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY1809 @ SY1808 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1804 ) @ SY1805 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY1809 @ SY1808 @ SY1805 @ SY1804 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1804 ) @ SY1805 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1808 ) @ SY1809 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(668,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(669,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(670,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(671,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(672,plain,
! [SV168: $i,SV96: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SV168 ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV96 ) @ SV168 ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(673,plain,
! [SV97: $i] :
( ( ( ~ ( linorder @ SV97 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) )
| ~ ! [SY1580: $i,SY1581: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1580 ) @ SY1581 ) )
| ( ( ti @ SV97 @ SY1580 )
= ( ti @ SV97 @ SY1581 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1581 ) @ SY1580 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(674,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(675,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(676,plain,
! [SV169: $i,SV98: $i] :
( ( ! [SY1810: $i] :
~ ( ~ ! [SY1811: $i,SY1812: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1812 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1812 @ SY1810 )
!= ( hAPP @ SV98 @ SV169 @ SY1812 @ SY1811 ) )
| ( ( ti @ SV98 @ SY1810 )
= ( ti @ SV98 @ SY1811 ) ) )
| ~ ! [SY1813: $i,SY1814: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1814 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SY1810 )
!= ( ti @ SV98 @ SY1813 ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1814 @ SY1810 )
= ( hAPP @ SV98 @ SV169 @ SY1814 @ SY1813 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(677,plain,
! [SV99: $i,SV170: $i] :
( ( ! [SY1815: $i] :
~ ( ~ ! [SY1816: $i,SY1817: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1816 )
= ( ti @ arrow_1212486748le_alt @ SY1817 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1817 )
= ( ti @ arrow_1212486748le_alt @ SY1815 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1816 )
= ( ti @ arrow_1212486748le_alt @ SY1815 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1816 ) @ SY1817 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1817 @ SY1816 @ SY1815 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1817 ) @ SY1815 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1817 @ SY1816 @ SY1815 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1816 ) @ SY1817 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1817 @ SY1816 @ SY1815 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1817 ) @ SY1815 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1817 @ SY1816 @ SY1815 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1816 ) @ SY1817 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1817 ) @ SY1815 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
| ~ ! [SY1818: $i,SY1819: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1818 )
= ( ti @ arrow_1212486748le_alt @ SY1819 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1819 )
= ( ti @ arrow_1212486748le_alt @ SY1815 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1818 )
= ( ti @ arrow_1212486748le_alt @ SY1815 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1818 ) @ SY1819 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1819 @ SY1818 @ SY1815 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1819 ) @ SY1815 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1819 @ SY1818 @ SY1815 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1818 ) @ SY1819 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1819 @ SY1818 @ SY1815 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1819 ) @ SY1815 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1819 @ SY1818 @ SY1815 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1819 ) @ SY1815 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1818 ) @ SY1819 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(678,plain,
! [SV100: $i] :
( ( ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1594 ) @ SY1595 ) )
| ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1595 @ SY1594 ) ) )
| ~ ! [SY1596: $i,SY1597: $i] :
( ~ ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1597 @ SY1596 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1596 ) @ SY1597 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(679,plain,
! [SV101: $i] :
( ( ~ ! [SY1598: $i,SY1599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( sK26_X1 @ SY1599 @ SY1598 @ SV101 ) ) )
| ! [SY1600: $i,SY1601: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( hAPP @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) @ ( hAPP @ SV101 @ ( fun @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) ) @ ( product_Pair @ SV101 @ SY1598 ) @ SY1600 ) @ SY1601 ) ) ) )
| ~ ! [SY1602: $i,SY1603: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ ( hAPP @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) @ ( hAPP @ SV101 @ ( fun @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) ) @ ( product_Pair @ SV101 @ SY1602 ) @ ( sK24_A_2 @ SY1603 @ SY1602 @ SV101 ) ) @ ( sK25_SY1332 @ SY1603 @ SY1602 @ SV101 ) ) ) )
| ! [SY1604: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ SY1604 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(680,plain,
! [SV102: $i,SV171: $i] :
( ( ! [SY1820: $i,SY1821: $i] :
~ ( ~ ! [SY1822: $i,SY1823: $i] :
( ( ( ti @ SV171 @ SY1820 )
!= ( ti @ SV171 @ SY1822 ) )
| ( ( ti @ SV102 @ SY1821 )
!= ( ti @ SV102 @ SY1823 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1820 ) @ SY1821 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1822 ) @ SY1823 ) ) )
| ~ ~ ( ~ ! [SY1824: $i] :
( ! [SY1825: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1820 ) @ SY1821 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1824 ) @ SY1825 ) )
| ( ( ti @ SV171 @ SY1820 )
= ( ti @ SV171 @ SY1824 ) ) )
| ~ ! [SY1826: $i,SY1827: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1820 ) @ SY1821 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1826 ) @ SY1827 ) )
| ( ( ti @ SV102 @ SY1821 )
= ( ti @ SV102 @ SY1827 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(681,plain,
! [SV172: $i,SV103: $i] :
( ( ! [SY1828: $i,SY1829: $i] :
~ ( ~ ! [SY1830: $i,SY1831: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY1830 ) @ SY1831 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1829 ) @ SY1831 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1828 ) @ SY1831 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY1830 @ SY1829 )
!= ( hAPP @ SV103 @ SV172 @ SY1830 @ SY1828 ) )
| ( ( ti @ SV103 @ SY1829 )
= ( ti @ SV103 @ SY1828 ) ) )
| ~ ! [SY1832: $i,SY1833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY1832 ) @ SY1833 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1829 ) @ SY1833 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1828 ) @ SY1833 ) )
| ( ( ti @ SV103 @ SY1829 )
!= ( ti @ SV103 @ SY1828 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY1832 @ SY1829 )
= ( hAPP @ SV103 @ SV172 @ SY1832 @ SY1828 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(682,plain,
! [SV173: $i,SV104: $i] :
( ( ! [SY1834: $i] :
( ~ ( ( ( hAPP @ SV104 @ SV173 @ SY1834 @ ( sK7_X_1 @ SY1834 @ SV173 @ SV104 ) )
!= ( hAPP @ SV104 @ SV173 @ SY1834 @ ( sK8_SY1309 @ SY1834 @ SV173 @ SV104 ) ) )
| ~ ( ( ( ti @ SV104 @ ( sK7_X_1 @ SY1834 @ SV173 @ SV104 ) )
!= ( ti @ SV104 @ ( sK8_SY1309 @ SY1834 @ SV173 @ SV104 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SY1834 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(683,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(684,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(685,plain,
! [SV174: $i,SV105: $i] :
( ( ~ ( ~ ! [SY1835: $i,SY1836: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1836 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1835 ) ) )
| ~ ! [SY1837: $i,SY1838: $i] :
( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1838 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1837 ) )
| ~ ( ~ ! [SY1839: $i,SY1840: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1838 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1837 ) ) )
| ~ ! [SY1841: $i,SY1842: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1837 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1838 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(686,plain,
! [SV175: $i,SV106: $i] :
( ( ~ ( ~ ! [SY1843: $i,SY1844: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1843 ) @ SY1844 ) ) )
| ~ ! [SY1845: $i,SY1846: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1845 ) @ SY1846 ) )
| ! [SY1847: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1847 ) @ SY1846 ) )
| ! [SY1848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1848 ) @ SY1846 ) )
| ( ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1847 )
!= ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1848 ) )
| ( ( ti @ SV106 @ SY1847 )
= ( ti @ SV106 @ SY1848 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(687,plain,
! [SV176: $i,SV107: $i] :
( ( ! [SY1849: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SY1850: $i,SY1851: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1850 )
= ( ti @ arrow_1212486748le_alt @ SY1851 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1851 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1851 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1850 ) @ SY1851 ) ) ) )
| ~ ! [SY1852: $i,SY1853: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1852 )
= ( ti @ arrow_1212486748le_alt @ SY1853 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1852 ) @ SV176 ) ) @ SY1849 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1853 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1852 ) @ SY1853 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1854: $i,SY1855: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1854 )
= ( ti @ arrow_1212486748le_alt @ SY1855 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1855 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1855 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1855 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1854 ) @ SY1855 ) ) ) )
| ~ ! [SY1856: $i,SY1857: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1856 )
= ( ti @ arrow_1212486748le_alt @ SY1857 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1857 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1857 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SY1849 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1856 ) @ SY1857 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1858: $i,SY1859: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1858 )
= ( ti @ arrow_1212486748le_alt @ SY1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1859 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1858 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1859 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1858 ) @ SY1859 ) ) ) )
| ~ ! [SY1860: $i,SY1861: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1860 )
= ( ti @ arrow_1212486748le_alt @ SY1861 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1861 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1860 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SY1849 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1860 ) @ SY1861 ) ) ) ) )
| ~ ~ ( ~ ! [SY1862: $i,SY1863: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1862 )
= ( ti @ arrow_1212486748le_alt @ SY1863 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1863 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1862 ) ) @ SY1849 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1863 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1862 ) @ SY1863 ) ) ) )
| ~ ! [SY1864: $i,SY1865: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1864 )
= ( ti @ arrow_1212486748le_alt @ SY1865 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1865 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1864 ) ) @ SY1849 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SY1849 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1864 ) @ SY1865 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1866: $i,SY1867: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1866 )
= ( ti @ arrow_1212486748le_alt @ SY1867 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1866 ) @ SV176 ) ) @ SY1849 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1867 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1867 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1866 ) @ SY1867 ) ) ) )
| ~ ! [SY1868: $i,SY1869: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1868 )
= ( ti @ arrow_1212486748le_alt @ SY1869 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1868 ) @ SV176 ) ) @ SY1849 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1869 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SY1849 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1868 ) @ SY1869 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1870: $i,SY1871: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1870 )
= ( ti @ arrow_1212486748le_alt @ SY1871 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1870 ) @ SV176 ) ) @ SY1849 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1870 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1871 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1870 ) @ SY1871 ) ) ) )
| ~ ! [SY1872: $i,SY1873: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1872 )
= ( ti @ arrow_1212486748le_alt @ SY1873 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1872 ) @ SV176 ) ) @ SY1849 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1872 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SY1849 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1872 ) @ SY1873 ) ) ) ) )
| ~ ~ ( ~ ! [SY1874: $i,SY1875: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1874 )
= ( ti @ arrow_1212486748le_alt @ SY1875 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1874 ) @ SV176 ) ) @ SY1849 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1874 ) ) @ SY1849 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1875 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1874 ) @ SY1875 ) ) ) )
| ~ ! [SY1876: $i,SY1877: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1876 )
= ( ti @ arrow_1212486748le_alt @ SY1877 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1876 ) @ SV176 ) ) @ SY1849 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1876 ) ) @ SY1849 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SY1849 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1876 ) @ SY1877 ) ) ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1878: $i,SY1879: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1878 )
= ( ti @ arrow_1212486748le_alt @ SY1879 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1878 ) @ SY1879 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY1880: $i,SY1881: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1880 )
= ( ti @ arrow_1212486748le_alt @ SY1881 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1880 ) @ SY1881 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1881 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1880 ) @ SV176 ) ) @ SY1849 ) ) ) )
| ~ ~ ( ~ ! [SY1882: $i,SY1883: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1882 )
= ( ti @ arrow_1212486748le_alt @ SY1883 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1882 ) @ SY1883 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1883 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1883 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1882 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1882 ) ) @ SY1849 ) ) )
| ~ ! [SY1884: $i,SY1885: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1884 )
= ( ti @ arrow_1212486748le_alt @ SY1885 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1849 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SY1849 ) @ SY1884 ) @ SY1885 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1885 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1885 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SY1849 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(688,plain,
! [SV108: $i,SV177: $i] :
( ( ~ ( ~ ! [SY1886: $i,SY1887: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1886 )
= ( ti @ arrow_1212486748le_alt @ SY1887 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
| ~ ! [SY1888: $i,SY1889: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1888 )
= ( ti @ arrow_1212486748le_alt @ SY1889 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(689,plain,
! [SV109: $i,SV178: $i] :
( ( ! [SY1890: $i,SY1891: $i,SY1892: $i,SY1893: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1892 )
= ( ti @ arrow_1212486748le_alt @ SY1893 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1890 )
= ( ti @ arrow_1212486748le_alt @ SY1891 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1892 )
= ( ti @ arrow_1212486748le_alt @ SY1891 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1893 )
= ( ti @ arrow_1212486748le_alt @ SY1890 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1892 ) @ SY1893 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY1893 @ SY1892 @ SY1891 @ SY1890 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1890 ) @ SY1891 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY1893 @ SY1892 @ SY1891 @ SY1890 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1892 ) @ SY1893 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY1893 @ SY1892 @ SY1891 @ SY1890 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1890 ) @ SY1891 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY1893 @ SY1892 @ SY1891 @ SY1890 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1892 ) @ SY1893 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1890 ) @ SY1891 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(690,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SX1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK1_X_1 @ SX1 @ SX0 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(691,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(692,plain,
! [SV179: $i,SV110: $i,SV1: $i] :
( ( ( ti @ ( fun @ ( fun @ SV1 @ SV110 ) @ ( fun @ ( fun @ SV179 @ SV1 ) @ ( fun @ SV179 @ SV110 ) ) ) @ ( combb @ SV1 @ SV110 @ SV179 ) )
= ( combb @ SV1 @ SV110 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(693,plain,
! [SV180: $i,SV111: $i,SV2: $i] :
( ( ( ti @ ( fun @ ( fun @ SV2 @ ( fun @ SV111 @ SV180 ) ) @ ( fun @ SV111 @ ( fun @ SV2 @ SV180 ) ) ) @ ( combc @ SV2 @ SV111 @ SV180 ) )
= ( combc @ SV2 @ SV111 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(694,plain,
! [SV181: $i,SV113: $i,SV5: $i] :
( ( ( ti @ ( fun @ ( fun @ SV5 @ ( fun @ SV113 @ SV181 ) ) @ ( fun @ ( fun @ SV5 @ SV113 ) @ ( fun @ SV5 @ SV181 ) ) ) @ ( combs @ SV5 @ SV113 @ SV181 ) )
= ( combs @ SV5 @ SV113 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(695,plain,
! [SV11: $i] :
( ( ( ord @ SV11 )
= $false )
| ( ( ( ti @ ( fun @ SV11 @ ( fun @ SV11 @ bool ) ) @ ( ord_less @ SV11 ) )
= ( ord_less @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(696,plain,
! [SV12: $i] :
( ( ( top @ SV12 )
= $false )
| ( ( ( ti @ SV12 @ ( top_top @ SV12 ) )
= ( top_top @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(697,plain,
! [SV182: $i,SV118: $i,SV14: $i] :
( ( ( ti @ ( fun @ ( fun @ SV14 @ ( fun @ SV118 @ SV182 ) ) @ ( fun @ ( product_prod @ SV14 @ SV118 ) @ SV182 ) ) @ ( product_prod_rec @ SV14 @ SV118 @ SV182 ) )
= ( product_prod_rec @ SV14 @ SV118 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(698,plain,
! [SV183: $i,SV119: $i,SV17: $i] :
( ( ! [SY1894: $i] :
( ( hAPP @ SV17 @ SV119 @ ( ti @ ( fun @ SV17 @ SV119 ) @ SV183 ) @ SY1894 )
= ( hAPP @ SV17 @ SV119 @ SV183 @ SY1894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(699,plain,
! [SV184: $i,SV120: $i,SV18: $i] :
( ( ! [SY1895: $i] :
( ( hAPP @ SV18 @ SV120 @ SV184 @ ( ti @ SV18 @ SY1895 ) )
= ( hAPP @ SV18 @ SV120 @ SV184 @ SY1895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(700,plain,
! [SV185: $i,SV121: $i,SV19: $i] :
( ( ! [SY1896: $i] :
( ( ti @ SV19 @ ( hAPP @ SV121 @ SV19 @ SV185 @ SY1896 ) )
= ( hAPP @ SV121 @ SV19 @ SV185 @ SY1896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(701,plain,
! [SV186: $i,SV125: $i,SV24: $i] :
( ( ! [SY1897: $i,SY1898: $i,SY1899: $i] :
( ( hAPP @ ( product_prod @ SV24 @ SV125 ) @ SV186 @ ( hAPP @ ( fun @ SV24 @ ( fun @ SV125 @ SV186 ) ) @ ( fun @ ( product_prod @ SV24 @ SV125 ) @ SV186 ) @ ( product_prod_rec @ SV24 @ SV125 @ SV186 ) @ SY1897 ) @ ( hAPP @ SV125 @ ( product_prod @ SV24 @ SV125 ) @ ( hAPP @ SV24 @ ( fun @ SV125 @ ( product_prod @ SV24 @ SV125 ) ) @ ( product_Pair @ SV24 @ SV125 ) @ SY1898 ) @ SY1899 ) )
= ( hAPP @ SV125 @ SV186 @ ( hAPP @ SV24 @ ( fun @ SV125 @ SV186 ) @ SY1897 @ SY1898 ) @ SY1899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(702,plain,
! [SV25: $i,SV126: $i] :
( ( ( ~ ( top @ SV126 ) )
= $true )
| ( ( ! [SY1701: $i] :
( ( hAPP @ SV25 @ SV126 @ ( top_top @ ( fun @ SV25 @ SV126 ) ) @ SY1701 )
= ( top_top @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(703,plain,
! [SV26: $i] :
( ( ( top @ SV26 )
= $false )
| ( ( ! [SY1365: $i] :
~ ( hBOOL @ ( hAPP @ SV26 @ bool @ ( hAPP @ SV26 @ ( fun @ SV26 @ bool ) @ ( ord_less @ SV26 ) @ ( top_top @ SV26 ) ) @ SY1365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(704,plain,
! [SV27: $i] :
( ( ( linorder @ SV27 )
= $false )
| ( ( ! [SY1366: $i,SY1367: $i] :
( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SY1366 ) @ SY1367 ) )
| ( ( ti @ SV27 @ SY1366 )
= ( ti @ SV27 @ SY1367 ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SY1367 ) @ SY1366 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(705,plain,
! [SV28: $i] :
( ( ( preorder @ SV28 )
= $false )
| ( ( ! [SY1368: $i,SY1369: $i] :
( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SY1368 ) @ SY1369 ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SY1369 ) @ SY1368 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(706,plain,
! [SV29: $i] :
( ( ( order @ SV29 )
= $false )
| ( ( ! [SY1370: $i,SY1371: $i,SY1372: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1371 ) @ SY1372 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1370 ) @ SY1371 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY1370 ) @ SY1372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(707,plain,
! [SV30: $i] :
( ( ( preorder @ SV30 )
= $false )
| ( ( ! [SY1373: $i,SY1374: $i,SY1375: $i] :
( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1374 ) @ SY1375 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1375 ) @ SY1373 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY1374 ) @ SY1373 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(708,plain,
! [SV31: $i] :
( ( ( order @ SV31 )
= $false )
| ( ( ! [SY1376: $i,SY1377: $i,SY1378: $i] :
( ~ ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SY1377 ) @ SY1378 ) )
| ( SY1377 != SY1376 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SY1376 ) @ SY1378 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(709,plain,
! [SV32: $i] :
( ( ( ord @ SV32 )
= $false )
| ( ( ! [SY1379: $i,SY1380: $i,SY1381: $i] :
( ~ ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY1380 ) @ SY1381 ) )
| ( SY1381 != SY1379 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY1380 ) @ SY1379 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(710,plain,
! [SV33: $i] :
( ( ( order @ SV33 )
= $false )
| ( ( ! [SY1382: $i,SY1383: $i,SY1384: $i] :
( ( SY1383 != SY1384 )
| ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SY1382 ) @ SY1384 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SY1382 ) @ SY1383 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(711,plain,
! [SV34: $i] :
( ( ( ord @ SV34 )
= $false )
| ( ( ! [SY1385: $i,SY1386: $i,SY1387: $i] :
( ( SY1386 != SY1387 )
| ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY1387 ) @ SY1385 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY1386 ) @ SY1385 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(712,plain,
! [SV35: $i] :
( ( ( order @ SV35 )
= $false )
| ( ( ! [SY1388: $i,SY1389: $i] :
( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SY1388 ) @ SY1389 ) )
| ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SY1389 ) @ SY1388 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(713,plain,
! [SV36: $i] :
( ( ( preorder @ SV36 )
= $false )
| ( ( ! [SY1390: $i,SY1391: $i] :
( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SY1390 ) @ SY1391 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SY1391 ) @ SY1390 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(714,plain,
! [SV37: $i] :
( ( ( preorder @ SV37 )
= $false )
| ( ( ! [SY1392: $i,SY1393: $i,SY1394: $i] :
( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY1393 ) @ SY1394 ) )
| ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY1394 ) @ SY1393 ) )
| ( hBOOL @ SY1392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(715,plain,
! [SV38: $i] :
( ( ( order @ SV38 )
= $false )
| ( ( ! [SY1395: $i,SY1396: $i] :
( ~ ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SY1395 ) @ SY1396 ) )
| ( SY1396 != SY1395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(716,plain,
! [SV39: $i] :
( ( ( order @ SV39 )
= $false )
| ( ( ! [SY1397: $i,SY1398: $i] :
( ~ ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SY1397 ) @ SY1398 ) )
| ( SY1397 != SY1398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(717,plain,
! [SV40: $i] :
( ( ( preorder @ SV40 )
= $false )
| ( ( ! [SY1399: $i,SY1400: $i] :
( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SY1399 ) @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SY1400 ) @ SY1399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(718,plain,
! [SV41: $i] :
( ( ( preorder @ SV41 )
= $false )
| ( ( ! [SY1401: $i,SY1402: $i] :
( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SY1401 ) @ SY1402 ) )
| ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SY1402 ) @ SY1401 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(719,plain,
! [SV42: $i] :
( ( ( order @ SV42 )
= $false )
| ( ( ! [SY1403: $i,SY1404: $i] :
( ~ ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SY1403 ) @ SY1404 ) )
| ( SY1403 != SY1404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(720,plain,
! [SV43: $i] :
( ( ( linorder @ SV43 )
= $false )
| ( ( ! [SY1405: $i,SY1406: $i] :
( ( ( ti @ SV43 @ SY1405 )
= ( ti @ SV43 @ SY1406 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SY1405 ) @ SY1406 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SY1406 ) @ SY1405 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(721,plain,
! [SV44: $i] :
( ( ( linorder @ SV44 )
= $false )
| ( ( ! [SY1407: $i,SY1408: $i] :
( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SY1408 ) @ SY1407 ) )
| ( ( ti @ SV44 @ SY1407 )
= ( ti @ SV44 @ SY1408 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SY1407 ) @ SY1408 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(722,plain,
! [SV45: $i] :
( ( ( preorder @ SV45 )
= $false )
| ( ( ! [SY1409: $i] :
~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( ord_less @ SV45 ) @ SY1409 ) @ SY1409 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(723,plain,
! [SV187: $i,SV127: $i,SV47: $i] :
( ( ! [SY1900: $i,SY1901: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SY1901 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
| ( ( hAPP @ SV47 @ SV127 @ SY1901 @ SV187 )
!= ( ti @ SV127 @ SY1900 ) )
| ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SY1901 ) @ SY1900 )
= ( ti @ SV47 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(724,plain,
! [SV188: $i,SV128: $i,SV48: $i] :
( ( ! [SY1902: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV48 @ bool ) @ bool @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ ( fun @ SV48 @ bool ) @ bool ) @ ( inj_on @ SV48 @ SV128 ) @ SY1902 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) )
| ( ( hAPP @ SV128 @ SV48 @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) @ ( hAPP @ ( fun @ SV48 @ bool ) @ ( fun @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) ) @ ( hilbert_inv_into @ SV48 @ SV128 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) @ SY1902 ) @ ( hAPP @ SV48 @ SV128 @ SY1902 @ SV188 ) )
= ( ti @ SV48 @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(725,plain,
! [SV49: $i,SV189: $i,SV129: $i] :
( ( ! [SY1903: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ SV189 ) @ SY1903 ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV189 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) ) @ ( combb @ SV189 @ ( fun @ SV49 @ SV189 ) @ SV129 ) @ ( combk @ SV189 @ SV49 ) ) @ SY1903 ) ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(726,plain,
! [SV190: $i,SV130: $i,SV50: $i] :
( ( ! [SY1904: $i,SY1905: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SY1904 ) @ SY1905 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SV190 ) @ SY1905 ) )
| ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SY1905 ) @ SY1904 ) @ ( hAPP @ SV50 @ SV130 @ SY1904 @ SV190 ) )
= ( ti @ SV50 @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(727,plain,
! [SV191: $i,SV131: $i,SV51: $i] :
( ( ! [SY1906: $i,SY1907: $i,SY1908: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SY1907 ) @ SY1908 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SY1906 ) @ SY1908 ) )
| ( ( hAPP @ SV51 @ SV131 @ SY1907 @ SY1906 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SY1908 ) @ SY1907 ) @ SV191 )
= ( ti @ SV51 @ SY1906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(728,plain,
! [SV192: $i,SV132: $i,SV52: $i] :
( ( ! [SY1909: $i,SY1910: $i,SY1911: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SY1910 ) @ SY1911 ) )
| ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SY1909 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SY1911 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SY1909 ) @ SY1911 ) )
| ( ( hAPP @ SV52 @ SV132 @ SY1910 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SY1910 @ SY1909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(729,plain,
! [SV193: $i,SV133: $i,SV53: $i] :
( ( ! [SY1912: $i,SY1913: $i,SY1914: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SY1913 ) @ SY1914 ) )
| ( ( hAPP @ SV53 @ SV133 @ SY1913 @ SV193 )
!= ( hAPP @ SV53 @ SV133 @ SY1913 @ SY1912 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SY1912 ) @ SY1914 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SY1912 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(730,plain,
! [SV194: $i,SV135: $i,SV55: $i] :
( ( ! [SY1915: $i,SY1916: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SY1916 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
| ( ( hAPP @ SV55 @ SV135 @ SY1916 @ SV194 )
!= ( hAPP @ SV55 @ SV135 @ SY1916 @ SY1915 ) )
| ( ( ti @ SV55 @ SV194 )
= ( ti @ SV55 @ SY1915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(731,plain,
! [SV195: $i,SV136: $i,SV56: $i] :
( ( ! [SY1917: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SV136 ) @ SY1917 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) )
| ( ( hAPP @ SV56 @ SV136 @ SY1917 @ ( hAPP @ SV136 @ SV56 @ SV195 @ ( sK9_X_1 @ SY1917 @ SV195 @ SV136 @ SV56 ) ) )
!= ( ti @ SV136 @ ( sK9_X_1 @ SY1917 @ SV195 @ SV136 @ SV56 ) ) )
| ( ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SV136 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SY1917 )
= ( ti @ ( fun @ SV136 @ SV56 ) @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(732,plain,
! [SV137: $i,SV57: $i,SV196: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV196 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SV137 ) ) @ SV196 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV137 ) @ SV57 ) ) @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(733,plain,
! [SV197: $i,SV138: $i,SV58: $i] :
( ( ! [SY1918: $i] :
( ( ( hAPP @ SV58 @ SV138 @ SV197 @ ( sK6_X_1 @ SY1918 @ SV197 @ SV138 @ SV58 ) )
!= ( hAPP @ SV58 @ SV138 @ SY1918 @ ( sK6_X_1 @ SY1918 @ SV197 @ SV138 @ SV58 ) ) )
| ( ( ti @ ( fun @ SV58 @ SV138 ) @ SV197 )
= ( ti @ ( fun @ SV58 @ SV138 ) @ SY1918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(734,plain,
! [SV60: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV140 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV140 ) @ SV60 ) ) @ arrow_638930832le_Lin ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(735,plain,
! [SV61: $i,SV141: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV141 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV141 ) @ SV61 ) ) @ arrow_638930832le_Lin ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(736,plain,
! [SV62: $i,SV198: $i,SV142: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV142 )
= ( ti @ arrow_1212486748le_alt @ SV198 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV62 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV62 ) @ SV142 ) @ SV198 ) ) @ arrow_638930832le_Lin ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(737,plain,
! [SV63: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV63 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ arrow_1384031255e_indi ) @ SV63 ) ) @ arrow_1834574746e_Prof ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(738,plain,
! [SV199: $i,SV143: $i,SV64: $i] :
( ( ! [SY1919: $i,SY1920: $i,SY1921: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SY1919 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SY1920 ) @ SY1921 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SY1919 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SY1921 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SY1920 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(739,plain,
! [SV200: $i,SV144: $i,SV66: $i] :
( ( ! [SY1922: $i,SY1923: $i,SY1924: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SY1922 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SY1923 ) @ SY1924 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SY1923 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SY1922 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SY1924 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(740,plain,
! [SV201: $i,SV145: $i,SV67: $i] :
( ( ! [SY1925: $i,SY1926: $i,SY1927: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SY1925 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SY1926 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SY1927 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SY1926 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SY1925 @ SV201 ) ) @ SY1927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(741,plain,
! [SV202: $i,SV147: $i,SV69: $i] :
( ( ( hAPP @ ( fun @ SV69 @ ( fun @ SV147 @ bool ) ) @ ( fun @ ( fun @ SV69 @ SV147 ) @ bool ) @ ( hAPP @ ( fun @ SV69 @ bool ) @ ( fun @ ( fun @ SV69 @ ( fun @ SV147 @ bool ) ) @ ( fun @ ( fun @ SV69 @ SV147 ) @ bool ) ) @ ( pi @ SV69 @ SV147 ) @ SV202 ) @ ( hAPP @ ( fun @ SV147 @ bool ) @ ( fun @ SV69 @ ( fun @ SV147 @ bool ) ) @ ( combk @ ( fun @ SV147 @ bool ) @ SV69 ) @ ( top_top @ ( fun @ SV147 @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ SV69 @ SV147 ) @ bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(742,plain,
! [SV70: $i,SV148: $i] :
( ( ( ~ ( preorder @ SV148 ) )
= $true )
| ( ( preorder @ ( fun @ SV70 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(743,plain,
! [SV71: $i,SV149: $i] :
( ( ( ~ ( order @ SV149 ) )
= $true )
| ( ( order @ ( fun @ SV71 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(744,plain,
! [SV72: $i,SV150: $i] :
( ( ( ~ ( top @ SV150 ) )
= $true )
| ( ( top @ ( fun @ SV72 @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(745,plain,
! [SV73: $i,SV151: $i] :
( ( ( ~ ( ord @ SV151 ) )
= $true )
| ( ( ord @ ( fun @ SV73 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(746,plain,
! [SV203: $i,SV153: $i,SV75: $i] :
( ( ( hAPP @ SV75 @ SV75 @ ( hAPP @ SV75 @ ( fun @ SV75 @ SV75 ) @ ( hAPP @ bool @ ( fun @ SV75 @ ( fun @ SV75 @ SV75 ) ) @ ( if @ SV75 ) @ fTrue ) @ SV153 ) @ SV203 )
= ( ti @ SV75 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(747,plain,
! [SV204: $i,SV154: $i,SV76: $i] :
( ( ( hAPP @ SV76 @ SV76 @ ( hAPP @ SV76 @ ( fun @ SV76 @ SV76 ) @ ( hAPP @ bool @ ( fun @ SV76 @ ( fun @ SV76 @ SV76 ) ) @ ( if @ SV76 ) @ fFalse ) @ SV154 ) @ SV204 )
= ( ti @ SV76 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(748,plain,
! [SV205: $i,SV155: $i,SV78: $i] :
( ( ! [SY1928: $i,SY1929: $i,SY1930: $i] :
( ( hAPP @ SV78 @ SV155 @ ( hAPP @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) @ ( hAPP @ ( fun @ SV205 @ SV155 ) @ ( fun @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) ) @ ( combb @ SV205 @ SV155 @ SV78 ) @ SY1928 ) @ SY1929 ) @ SY1930 )
= ( hAPP @ SV205 @ SV155 @ SY1928 @ ( hAPP @ SV78 @ SV205 @ SY1929 @ SY1930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(749,plain,
! [SV206: $i,SV156: $i,SV79: $i] :
( ( ! [SY1931: $i,SY1932: $i,SY1933: $i] :
( ( hAPP @ SV79 @ SV156 @ ( hAPP @ SV206 @ ( fun @ SV79 @ SV156 ) @ ( hAPP @ ( fun @ SV79 @ ( fun @ SV206 @ SV156 ) ) @ ( fun @ SV206 @ ( fun @ SV79 @ SV156 ) ) @ ( combc @ SV79 @ SV206 @ SV156 ) @ SY1931 ) @ SY1932 ) @ SY1933 )
= ( hAPP @ SV206 @ SV156 @ ( hAPP @ SV79 @ ( fun @ SV206 @ SV156 ) @ SY1931 @ SY1933 ) @ SY1932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(750,plain,
! [SV207: $i,SV158: $i,SV81: $i] :
( ( ! [SY1934: $i] :
( ( hAPP @ SV81 @ SV158 @ ( hAPP @ SV158 @ ( fun @ SV81 @ SV158 ) @ ( combk @ SV158 @ SV81 ) @ SV207 ) @ SY1934 )
= ( ti @ SV158 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(751,plain,
! [SV208: $i,SV159: $i,SV82: $i] :
( ( ! [SY1935: $i,SY1936: $i,SY1937: $i] :
( ( hAPP @ SV82 @ SV159 @ ( hAPP @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) @ ( hAPP @ ( fun @ SV82 @ ( fun @ SV208 @ SV159 ) ) @ ( fun @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) ) @ ( combs @ SV82 @ SV208 @ SV159 ) @ SY1935 ) @ SY1936 ) @ SY1937 )
= ( hAPP @ SV208 @ SV159 @ ( hAPP @ SV82 @ ( fun @ SV208 @ SV159 ) @ SY1935 @ SY1937 ) @ ( hAPP @ SV82 @ SV208 @ SY1936 @ SY1937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(752,plain,
! [SV209: $i,SV160: $i,SV84: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV84 @ bool @ ( hAPP @ SV84 @ ( fun @ SV84 @ bool ) @ ( fequal @ SV84 ) @ SV160 ) @ SV209 ) )
| ( ( ti @ SV84 @ SV160 )
= ( ti @ SV84 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(753,plain,
! [SV210: $i,SV161: $i,SV85: $i] :
( ( ( ( ti @ SV85 @ SV161 )
!= ( ti @ SV85 @ SV210 ) )
| ( hBOOL @ ( hAPP @ SV85 @ bool @ ( hAPP @ SV85 @ ( fun @ SV85 @ bool ) @ ( fequal @ SV85 ) @ SV161 ) @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(754,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
| ~ ~ ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
| ~ ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1776 ) @ SY1777 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1777 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1776 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(755,plain,
! [SV87: $i,SV163: $i,SV211: $i] :
( ( ! [SY1938: $i] :
~ ( ~ ! [SY1939: $i,SY1940: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1939 )
= ( ti @ arrow_1212486748le_alt @ SY1940 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SY1938 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1939 ) @ SY1940 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY1940 @ SY1939 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SY1938 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY1940 @ SY1939 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1939 ) @ SY1940 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY1940 @ SY1939 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SY1938 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY1940 @ SY1939 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1939 ) @ SY1940 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SY1938 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
| ~ ! [SY1941: $i,SY1942: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1941 )
= ( ti @ arrow_1212486748le_alt @ SY1942 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SY1938 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1941 ) @ SY1942 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY1942 @ SY1941 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SY1938 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY1942 @ SY1941 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1941 ) @ SY1942 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY1942 @ SY1941 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SY1938 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY1942 @ SY1941 @ SY1938 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SY1938 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1941 ) @ SY1942 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(756,plain,
! [SV212: $i,SV164: $i,SV88: $i] :
( ( ! [SY1943: $i] :
~ ( ~ ! [SY1944: $i] :
( ! [SY1945: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SY1943 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY1944 ) @ SY1945 ) )
| ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SY1944 ) ) )
| ~ ! [SY1946: $i,SY1947: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SY1943 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY1946 ) @ SY1947 ) )
| ( ( ti @ SV88 @ SY1943 )
= ( ti @ SV88 @ SY1947 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(757,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
| ~ ~ ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
| ~ ! [SY1802: $i,SY1803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1802 ) @ SY1803 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1803 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1802 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(758,plain,
! [SV90: $i] :
( ( ( linorder @ SV90 )
= $false )
| ( ( ~ ( ~ ! [SY1551: $i,SY1552: $i] :
( ( ( ti @ SV90 @ SY1551 )
= ( ti @ SV90 @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1551 ) @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1552 ) @ SY1551 ) ) )
| ~ ~ ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) )
| ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(759,plain,
! [SV91: $i] :
( ( ~ ! [SY1557: $i,SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1558 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1557 ) @ SV91 ) ) @ SY1558 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1557 ) ) @ SY1558 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(760,plain,
! [SV91: $i] :
( ( ~ ! [SY1559: $i,SY1560: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1560 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1559 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1559 ) ) @ SY1560 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1559 ) @ SV91 ) ) @ SY1560 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(761,plain,
! [SV92: $i] :
( ( ( top @ SV92 )
= $false )
| ( ( ~ ( ~ ! [SY1561: $i] :
( ( ( ti @ SV92 @ SY1561 )
= ( top_top @ SV92 ) )
| ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1561 ) @ ( top_top @ SV92 ) ) ) )
| ~ ! [SY1562: $i] :
( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1562 ) @ ( top_top @ SV92 ) ) )
| ( ( ti @ SV92 @ SY1562 )
!= ( top_top @ SV92 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(762,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(763,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(764,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ! [SX1: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SX0 ) ) @ ( sK17_SY1315 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK15_X_1 @ SX0 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(765,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK14_I @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX2 ) @ SX3 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(766,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(767,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(768,plain,
! [SV93: $i] :
( ( ( linorder @ SV93 )
= $false )
| ( ( ~ ( ~ ! [SY1563: $i,SY1564: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1563 ) @ SY1564 ) )
| ( ( ti @ SV93 @ SY1564 )
!= ( ti @ SV93 @ SY1563 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1564 ) @ SY1563 ) ) )
| ~ ! [SY1565: $i,SY1566: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1565 ) @ SY1566 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1566 ) @ SY1565 ) )
| ( ( ti @ SV93 @ SY1566 )
= ( ti @ SV93 @ SY1565 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(769,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SV166 @ SV94 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(770,plain,
! [SV95: $i,SV167: $i,SV213: $i] :
( ( ! [SY1948: $i] :
~ ( ~ ! [SY1949: $i,SY1950: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1949 )
= ( ti @ arrow_1212486748le_alt @ SY1950 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SY1948 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1949 )
= ( ti @ arrow_1212486748le_alt @ SY1948 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1950 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1949 ) @ SY1950 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY1950 @ SY1949 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SY1948 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY1950 @ SY1949 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1949 ) @ SY1950 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY1950 @ SY1949 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SY1948 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY1950 @ SY1949 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1949 ) @ SY1950 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SY1948 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
| ~ ! [SY1951: $i,SY1952: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1951 )
= ( ti @ arrow_1212486748le_alt @ SY1952 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SY1948 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1951 )
= ( ti @ arrow_1212486748le_alt @ SY1948 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1952 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1951 ) @ SY1952 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY1952 @ SY1951 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SY1948 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY1952 @ SY1951 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1951 ) @ SY1952 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY1952 @ SY1951 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SY1948 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY1952 @ SY1951 @ SY1948 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SY1948 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1951 ) @ SY1952 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(771,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SX0 ) @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SX0 ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK20_X_1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SX0 ) ) @ ( sK23_SY1327 @ SX0 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK21_SY1318 @ SX0 ) ) ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(772,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SX0 ) )
| ! [SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX1 ) @ arrow_1834574746e_Prof ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK19_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX1 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ ( sK18_I @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SX3 ) @ SX4 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(773,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( ti @ bool @ SX0 ) )
| ( hBOOL @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(774,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ SX0 )
| ( hBOOL @ ( ti @ bool @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(775,plain,
! [SV168: $i,SV96: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SV168 ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV96 ) @ SV168 ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(776,plain,
! [SV97: $i] :
( ( ( linorder @ SV97 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) )
| ~ ! [SY1580: $i,SY1581: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1580 ) @ SY1581 ) )
| ( ( ti @ SV97 @ SY1580 )
= ( ti @ SV97 @ SY1581 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1581 ) @ SY1580 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(777,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(778,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(779,plain,
! [SV214: $i,SV169: $i,SV98: $i] :
( ( ~ ( ~ ! [SY1953: $i,SY1954: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1954 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1954 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SY1954 @ SY1953 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SY1953 ) ) )
| ~ ! [SY1955: $i,SY1956: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1956 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SY1955 ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1956 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SY1956 @ SY1955 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(780,plain,
! [SV99: $i,SV170: $i,SV215: $i] :
( ( ~ ( ~ ! [SY1957: $i,SY1958: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SY1958 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1958 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
| ~ ! [SY1959: $i,SY1960: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SY1960 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1960 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(781,plain,
! [SV100: $i] :
( ( ~ ! [SY1594: $i,SY1595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1594 ) @ SY1595 ) )
| ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1595 @ SY1594 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(782,plain,
! [SV100: $i] :
( ( ~ ! [SY1596: $i,SY1597: $i] :
( ~ ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1597 @ SY1596 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1596 ) @ SY1597 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(783,plain,
! [SV101: $i] :
( ( ~ ! [SY1598: $i,SY1599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( sK26_X1 @ SY1599 @ SY1598 @ SV101 ) ) )
| ! [SY1600: $i,SY1601: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( hAPP @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) @ ( hAPP @ SV101 @ ( fun @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) ) @ ( product_Pair @ SV101 @ SY1598 ) @ SY1600 ) @ SY1601 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(784,plain,
! [SV101: $i] :
( ( ~ ! [SY1602: $i,SY1603: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ ( hAPP @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) @ ( hAPP @ SV101 @ ( fun @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) ) @ ( product_Pair @ SV101 @ SY1602 ) @ ( sK24_A_2 @ SY1603 @ SY1602 @ SV101 ) ) @ ( sK25_SY1332 @ SY1603 @ SY1602 @ SV101 ) ) ) )
| ! [SY1604: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ SY1604 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(785,plain,
! [SV102: $i,SV216: $i,SV171: $i] :
( ( ! [SY1961: $i] :
~ ( ~ ! [SY1962: $i,SY1963: $i] :
( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SY1962 ) )
| ( ( ti @ SV102 @ SY1961 )
!= ( ti @ SV102 @ SY1963 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SY1961 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1962 ) @ SY1963 ) ) )
| ~ ~ ( ~ ! [SY1964: $i] :
( ! [SY1965: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SY1961 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1964 ) @ SY1965 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY1964 ) ) )
| ~ ! [SY1966: $i,SY1967: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SY1961 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY1966 ) @ SY1967 ) )
| ( ( ti @ SV102 @ SY1961 )
= ( ti @ SV102 @ SY1967 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(786,plain,
! [SV217: $i,SV172: $i,SV103: $i] :
( ( ! [SY1968: $i] :
~ ( ~ ! [SY1969: $i,SY1970: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY1969 ) @ SY1970 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1968 ) @ SY1970 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY1970 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY1969 @ SY1968 )
!= ( hAPP @ SV103 @ SV172 @ SY1969 @ SV217 ) )
| ( ( ti @ SV103 @ SY1968 )
= ( ti @ SV103 @ SV217 ) ) )
| ~ ! [SY1971: $i,SY1972: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY1971 ) @ SY1972 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SY1968 ) @ SY1972 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY1972 ) )
| ( ( ti @ SV103 @ SY1968 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY1971 @ SY1968 )
= ( hAPP @ SV103 @ SV172 @ SY1971 @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(787,plain,
! [SV218: $i,SV173: $i,SV104: $i] :
( ( ~ ( ( ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) )
| ~ ( ( ( ti @ SV104 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( ti @ SV104 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(788,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(789,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[684]) ).
thf(790,plain,
! [SV174: $i,SV105: $i] :
( ( ~ ! [SY1835: $i,SY1836: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1836 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1835 ) ) )
| ~ ! [SY1837: $i,SY1838: $i] :
( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1838 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1837 ) )
| ~ ( ~ ! [SY1839: $i,SY1840: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1838 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1837 ) ) )
| ~ ! [SY1841: $i,SY1842: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1837 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1838 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(791,plain,
! [SV175: $i,SV106: $i] :
( ( ~ ! [SY1843: $i,SY1844: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1843 ) @ SY1844 ) ) )
| ~ ! [SY1845: $i,SY1846: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1845 ) @ SY1846 ) )
| ! [SY1847: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1847 ) @ SY1846 ) )
| ! [SY1848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1848 ) @ SY1846 ) )
| ( ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1847 )
!= ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1848 ) )
| ( ( ti @ SV106 @ SY1847 )
= ( ti @ SV106 @ SY1848 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(792,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
| ~ ~ ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(793,plain,
! [SV108: $i,SV177: $i] :
( ( ~ ! [SY1886: $i,SY1887: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1886 )
= ( ti @ arrow_1212486748le_alt @ SY1887 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
| ~ ! [SY1888: $i,SY1889: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1888 )
= ( ti @ arrow_1212486748le_alt @ SY1889 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(794,plain,
! [SV109: $i,SV178: $i,SV220: $i] :
( ( ! [SY2009: $i,SY2010: $i,SY2011: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2010 )
= ( ti @ arrow_1212486748le_alt @ SY2011 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SY2009 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2010 )
= ( ti @ arrow_1212486748le_alt @ SY2009 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2011 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2010 ) @ SY2011 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY2011 @ SY2010 @ SY2009 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SY2009 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY2011 @ SY2010 @ SY2009 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2010 ) @ SY2011 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY2011 @ SY2010 @ SY2009 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SY2009 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY2011 @ SY2010 @ SY2009 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2010 ) @ SY2011 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SY2009 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(795,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SX1 @ SX0 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ ( sK1_X_1 @ SX1 @ SX0 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(796,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SX0 ) @ SX1 ) )
| ! [SX2: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SX2 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX0 @ SX2 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(797,plain,
! [SV221: $i,SV183: $i,SV119: $i,SV17: $i] :
( ( ( hAPP @ SV17 @ SV119 @ ( ti @ ( fun @ SV17 @ SV119 ) @ SV183 ) @ SV221 )
= ( hAPP @ SV17 @ SV119 @ SV183 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(798,plain,
! [SV222: $i,SV184: $i,SV120: $i,SV18: $i] :
( ( ( hAPP @ SV18 @ SV120 @ SV184 @ ( ti @ SV18 @ SV222 ) )
= ( hAPP @ SV18 @ SV120 @ SV184 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(799,plain,
! [SV223: $i,SV185: $i,SV121: $i,SV19: $i] :
( ( ( ti @ SV19 @ ( hAPP @ SV121 @ SV19 @ SV185 @ SV223 ) )
= ( hAPP @ SV121 @ SV19 @ SV185 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(800,plain,
! [SV224: $i,SV186: $i,SV125: $i,SV24: $i] :
( ( ! [SY2012: $i,SY2013: $i] :
( ( hAPP @ ( product_prod @ SV24 @ SV125 ) @ SV186 @ ( hAPP @ ( fun @ SV24 @ ( fun @ SV125 @ SV186 ) ) @ ( fun @ ( product_prod @ SV24 @ SV125 ) @ SV186 ) @ ( product_prod_rec @ SV24 @ SV125 @ SV186 ) @ SV224 ) @ ( hAPP @ SV125 @ ( product_prod @ SV24 @ SV125 ) @ ( hAPP @ SV24 @ ( fun @ SV125 @ ( product_prod @ SV24 @ SV125 ) ) @ ( product_Pair @ SV24 @ SV125 ) @ SY2012 ) @ SY2013 ) )
= ( hAPP @ SV125 @ SV186 @ ( hAPP @ SV24 @ ( fun @ SV125 @ SV186 ) @ SV224 @ SY2012 ) @ SY2013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(801,plain,
! [SV25: $i,SV126: $i] :
( ( ( top @ SV126 )
= $false )
| ( ( ! [SY1701: $i] :
( ( hAPP @ SV25 @ SV126 @ ( top_top @ ( fun @ SV25 @ SV126 ) ) @ SY1701 )
= ( top_top @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(802,plain,
! [SV225: $i,SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV26 @ bool @ ( hAPP @ SV26 @ ( fun @ SV26 @ bool ) @ ( ord_less @ SV26 ) @ ( top_top @ SV26 ) ) @ SV225 ) ) )
= $true )
| ( ( top @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(803,plain,
! [SV226: $i,SV27: $i] :
( ( ( ! [SY2014: $i] :
( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SV226 ) @ SY2014 ) )
| ( ( ti @ SV27 @ SV226 )
= ( ti @ SV27 @ SY2014 ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SY2014 ) @ SV226 ) ) ) )
= $true )
| ( ( linorder @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(804,plain,
! [SV227: $i,SV28: $i] :
( ( ( ! [SY2015: $i] :
( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV227 ) @ SY2015 ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SY2015 ) @ SV227 ) ) ) )
= $true )
| ( ( preorder @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(805,plain,
! [SV228: $i,SV29: $i] :
( ( ( ! [SY2016: $i,SY2017: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SY2016 ) @ SY2017 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SY2016 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SY2017 ) ) ) )
= $true )
| ( ( order @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(806,plain,
! [SV229: $i,SV30: $i] :
( ( ( ! [SY2018: $i,SY2019: $i] :
( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY2018 ) @ SY2019 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY2019 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY2018 ) @ SV229 ) ) ) )
= $true )
| ( ( preorder @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(807,plain,
! [SV230: $i,SV31: $i] :
( ( ( ! [SY2020: $i,SY2021: $i] :
( ~ ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SY2020 ) @ SY2021 ) )
| ( SY2020 != SV230 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV230 ) @ SY2021 ) ) ) )
= $true )
| ( ( order @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(808,plain,
! [SV231: $i,SV32: $i] :
( ( ( ! [SY2022: $i,SY2023: $i] :
( ~ ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY2022 ) @ SY2023 ) )
| ( SY2023 != SV231 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SY2022 ) @ SV231 ) ) ) )
= $true )
| ( ( ord @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(809,plain,
! [SV232: $i,SV33: $i] :
( ( ( ! [SY2024: $i,SY2025: $i] :
( ( SY2024 != SY2025 )
| ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SY2025 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SY2024 ) ) ) )
= $true )
| ( ( order @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(810,plain,
! [SV233: $i,SV34: $i] :
( ( ( ! [SY2026: $i,SY2027: $i] :
( ( SY2026 != SY2027 )
| ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY2027 ) @ SV233 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY2026 ) @ SV233 ) ) ) )
= $true )
| ( ( ord @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(811,plain,
! [SV234: $i,SV35: $i] :
( ( ( ! [SY2028: $i] :
( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV234 ) @ SY2028 ) )
| ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SY2028 ) @ SV234 ) ) ) )
= $true )
| ( ( order @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(812,plain,
! [SV235: $i,SV36: $i] :
( ( ( ! [SY2029: $i] :
( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV235 ) @ SY2029 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SY2029 ) @ SV235 ) ) ) )
= $true )
| ( ( preorder @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(813,plain,
! [SV236: $i,SV37: $i] :
( ( ( ! [SY2030: $i,SY2031: $i] :
( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY2030 ) @ SY2031 ) )
| ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY2031 ) @ SY2030 ) )
| ( hBOOL @ SV236 ) ) )
= $true )
| ( ( preorder @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(814,plain,
! [SV237: $i,SV38: $i] :
( ( ( ! [SY2032: $i] :
( ~ ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SV237 ) @ SY2032 ) )
| ( SY2032 != SV237 ) ) )
= $true )
| ( ( order @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(815,plain,
! [SV238: $i,SV39: $i] :
( ( ( ! [SY2033: $i] :
( ~ ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SV238 ) @ SY2033 ) )
| ( SV238 != SY2033 ) ) )
= $true )
| ( ( order @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(816,plain,
! [SV239: $i,SV40: $i] :
( ( ( ! [SY2034: $i] :
( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV239 ) @ SY2034 ) )
| ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SY2034 ) @ SV239 ) ) ) )
= $true )
| ( ( preorder @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(817,plain,
! [SV240: $i,SV41: $i] :
( ( ( ! [SY2035: $i] :
( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV240 ) @ SY2035 ) )
| ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SY2035 ) @ SV240 ) ) ) )
= $true )
| ( ( preorder @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(818,plain,
! [SV241: $i,SV42: $i] :
( ( ( ! [SY2036: $i] :
( ~ ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SV241 ) @ SY2036 ) )
| ( SV241 != SY2036 ) ) )
= $true )
| ( ( order @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(819,plain,
! [SV242: $i,SV43: $i] :
( ( ( ! [SY2037: $i] :
( ( ( ti @ SV43 @ SV242 )
= ( ti @ SV43 @ SY2037 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SV242 ) @ SY2037 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SY2037 ) @ SV242 ) ) ) )
= $true )
| ( ( linorder @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(820,plain,
! [SV243: $i,SV44: $i] :
( ( ( ! [SY2038: $i] :
( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SY2038 ) @ SV243 ) )
| ( ( ti @ SV44 @ SV243 )
= ( ti @ SV44 @ SY2038 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SV243 ) @ SY2038 ) ) ) )
= $true )
| ( ( linorder @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(821,plain,
! [SV244: $i,SV45: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( ord_less @ SV45 ) @ SV244 ) @ SV244 ) ) )
= $true )
| ( ( preorder @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(822,plain,
! [SV245: $i,SV187: $i,SV127: $i,SV47: $i] :
( ( ! [SY2039: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SY2039 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
| ( ( hAPP @ SV47 @ SV127 @ SY2039 @ SV187 )
!= ( ti @ SV127 @ SV245 ) )
| ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SY2039 ) @ SV245 )
= ( ti @ SV47 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(823,plain,
! [SV188: $i,SV246: $i,SV128: $i,SV48: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV48 @ bool ) @ bool @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ ( fun @ SV48 @ bool ) @ bool ) @ ( inj_on @ SV48 @ SV128 ) @ SV246 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) )
| ( ( hAPP @ SV128 @ SV48 @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) @ ( hAPP @ ( fun @ SV48 @ bool ) @ ( fun @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) ) @ ( hilbert_inv_into @ SV48 @ SV128 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) @ SV246 ) @ ( hAPP @ SV48 @ SV128 @ SV246 @ SV188 ) )
= ( ti @ SV48 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(824,plain,
! [SV49: $i,SV247: $i,SV189: $i,SV129: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ SV189 ) @ SV247 ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV189 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) ) @ ( combb @ SV189 @ ( fun @ SV49 @ SV189 ) @ SV129 ) @ ( combk @ SV189 @ SV49 ) ) @ SV247 ) ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(825,plain,
! [SV190: $i,SV248: $i,SV130: $i,SV50: $i] :
( ( ! [SY2040: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SV248 ) @ SY2040 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SV190 ) @ SY2040 ) )
| ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SY2040 ) @ SV248 ) @ ( hAPP @ SV50 @ SV130 @ SV248 @ SV190 ) )
= ( ti @ SV50 @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(826,plain,
! [SV191: $i,SV249: $i,SV131: $i,SV51: $i] :
( ( ! [SY2041: $i,SY2042: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SY2041 ) @ SY2042 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SY2042 ) )
| ( ( hAPP @ SV51 @ SV131 @ SY2041 @ SV249 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SY2042 ) @ SY2041 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(827,plain,
! [SV250: $i,SV192: $i,SV132: $i,SV52: $i] :
( ( ! [SY2043: $i,SY2044: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SY2043 ) @ SY2044 ) )
| ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SY2044 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SY2044 ) )
| ( ( hAPP @ SV52 @ SV132 @ SY2043 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SY2043 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(828,plain,
! [SV251: $i,SV193: $i,SV133: $i,SV53: $i] :
( ( ! [SY2045: $i,SY2046: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SY2045 ) @ SY2046 ) )
| ( ( hAPP @ SV53 @ SV133 @ SY2045 @ SV193 )
!= ( hAPP @ SV53 @ SV133 @ SY2045 @ SV251 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SY2046 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SY2046 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(829,plain,
! [SV252: $i,SV194: $i,SV135: $i,SV55: $i] :
( ( ! [SY2047: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SY2047 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
| ( ( hAPP @ SV55 @ SV135 @ SY2047 @ SV194 )
!= ( hAPP @ SV55 @ SV135 @ SY2047 @ SV252 ) )
| ( ( ti @ SV55 @ SV194 )
= ( ti @ SV55 @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(830,plain,
! [SV195: $i,SV253: $i,SV136: $i,SV56: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SV136 ) @ SV253 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) )
| ( ( hAPP @ SV56 @ SV136 @ SV253 @ ( hAPP @ SV136 @ SV56 @ SV195 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
!= ( ti @ SV136 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
| ( ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SV136 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SV253 )
= ( ti @ ( fun @ SV136 @ SV56 ) @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(831,plain,
! [SV137: $i,SV57: $i,SV196: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV196 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SV137 ) ) @ SV196 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV137 ) @ SV57 ) ) @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(832,plain,
! [SV254: $i,SV197: $i,SV138: $i,SV58: $i] :
( ( ( ( hAPP @ SV58 @ SV138 @ SV197 @ ( sK6_X_1 @ SV254 @ SV197 @ SV138 @ SV58 ) )
!= ( hAPP @ SV58 @ SV138 @ SV254 @ ( sK6_X_1 @ SV254 @ SV197 @ SV138 @ SV58 ) ) )
| ( ( ti @ ( fun @ SV58 @ SV138 ) @ SV197 )
= ( ti @ ( fun @ SV58 @ SV138 ) @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(833,plain,
! [SV60: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV140 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV140 ) @ SV60 ) ) @ arrow_638930832le_Lin ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(834,plain,
! [SV61: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV141 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV141 ) @ SV61 ) ) @ arrow_638930832le_Lin ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(835,plain,
! [SV62: $i,SV198: $i,SV142: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV142 )
= ( ti @ arrow_1212486748le_alt @ SV198 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV62 ) @ arrow_638930832le_Lin ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV62 ) @ SV142 ) @ SV198 ) ) @ arrow_638930832le_Lin ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(836,plain,
! [SV199: $i,SV255: $i,SV143: $i,SV64: $i] :
( ( ! [SY2048: $i,SY2049: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SV255 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SY2048 ) @ SY2049 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SV255 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SY2049 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SY2048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(837,plain,
! [SV200: $i,SV256: $i,SV144: $i,SV66: $i] :
( ( ! [SY2050: $i,SY2051: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SV256 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SY2050 ) @ SY2051 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SY2050 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SV256 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SY2051 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(838,plain,
! [SV201: $i,SV257: $i,SV145: $i,SV67: $i] :
( ( ! [SY2052: $i,SY2053: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SV257 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SY2052 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SY2053 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SY2052 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SV257 @ SV201 ) ) @ SY2053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(839,plain,
! [SV70: $i,SV148: $i] :
( ( ( preorder @ SV148 )
= $false )
| ( ( preorder @ ( fun @ SV70 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(840,plain,
! [SV71: $i,SV149: $i] :
( ( ( order @ SV149 )
= $false )
| ( ( order @ ( fun @ SV71 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(841,plain,
! [SV72: $i,SV150: $i] :
( ( ( top @ SV150 )
= $false )
| ( ( top @ ( fun @ SV72 @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(842,plain,
! [SV73: $i,SV151: $i] :
( ( ( ord @ SV151 )
= $false )
| ( ( ord @ ( fun @ SV73 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(843,plain,
! [SV258: $i,SV205: $i,SV155: $i,SV78: $i] :
( ( ! [SY2054: $i,SY2055: $i] :
( ( hAPP @ SV78 @ SV155 @ ( hAPP @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) @ ( hAPP @ ( fun @ SV205 @ SV155 ) @ ( fun @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) ) @ ( combb @ SV205 @ SV155 @ SV78 ) @ SV258 ) @ SY2054 ) @ SY2055 )
= ( hAPP @ SV205 @ SV155 @ SV258 @ ( hAPP @ SV78 @ SV205 @ SY2054 @ SY2055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(844,plain,
! [SV259: $i,SV206: $i,SV156: $i,SV79: $i] :
( ( ! [SY2056: $i,SY2057: $i] :
( ( hAPP @ SV79 @ SV156 @ ( hAPP @ SV206 @ ( fun @ SV79 @ SV156 ) @ ( hAPP @ ( fun @ SV79 @ ( fun @ SV206 @ SV156 ) ) @ ( fun @ SV206 @ ( fun @ SV79 @ SV156 ) ) @ ( combc @ SV79 @ SV206 @ SV156 ) @ SV259 ) @ SY2056 ) @ SY2057 )
= ( hAPP @ SV206 @ SV156 @ ( hAPP @ SV79 @ ( fun @ SV206 @ SV156 ) @ SV259 @ SY2057 ) @ SY2056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(845,plain,
! [SV260: $i,SV207: $i,SV158: $i,SV81: $i] :
( ( ( hAPP @ SV81 @ SV158 @ ( hAPP @ SV158 @ ( fun @ SV81 @ SV158 ) @ ( combk @ SV158 @ SV81 ) @ SV207 ) @ SV260 )
= ( ti @ SV158 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(846,plain,
! [SV261: $i,SV208: $i,SV159: $i,SV82: $i] :
( ( ! [SY2058: $i,SY2059: $i] :
( ( hAPP @ SV82 @ SV159 @ ( hAPP @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) @ ( hAPP @ ( fun @ SV82 @ ( fun @ SV208 @ SV159 ) ) @ ( fun @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) ) @ ( combs @ SV82 @ SV208 @ SV159 ) @ SV261 ) @ SY2058 ) @ SY2059 )
= ( hAPP @ SV208 @ SV159 @ ( hAPP @ SV82 @ ( fun @ SV208 @ SV159 ) @ SV261 @ SY2059 ) @ ( hAPP @ SV82 @ SV208 @ SY2058 @ SY2059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(847,plain,
! [SV209: $i,SV160: $i,SV84: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV84 @ bool @ ( hAPP @ SV84 @ ( fun @ SV84 @ bool ) @ ( fequal @ SV84 ) @ SV160 ) @ SV209 ) ) )
= $true )
| ( ( ( ti @ SV84 @ SV160 )
= ( ti @ SV84 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(848,plain,
! [SV210: $i,SV161: $i,SV85: $i] :
( ( ( ( ( ti @ SV85 @ SV161 )
!= ( ti @ SV85 @ SV210 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV85 @ bool @ ( hAPP @ SV85 @ ( fun @ SV85 @ bool ) @ ( fequal @ SV85 ) @ SV161 ) @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(849,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
| ~ ~ ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(850,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
| ~ ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1776 ) @ SY1777 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1777 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1776 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(851,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ~ ( ~ ! [SY2060: $i,SY2061: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2060 )
= ( ti @ arrow_1212486748le_alt @ SY2061 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
| ~ ! [SY2062: $i,SY2063: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2062 )
= ( ti @ arrow_1212486748le_alt @ SY2063 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(852,plain,
! [SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ~ ( ~ ! [SY2064: $i] :
( ! [SY2065: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2064 ) @ SY2065 ) )
| ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SY2064 ) ) )
| ~ ! [SY2066: $i,SY2067: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2066 ) @ SY2067 ) )
| ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SY2067 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(853,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
| ~ ~ ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(854,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
| ~ ! [SY1802: $i,SY1803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1802 ) @ SY1803 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1803 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1802 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(855,plain,
! [SV90: $i] :
( ( ( ~ ! [SY1551: $i,SY1552: $i] :
( ( ( ti @ SV90 @ SY1551 )
= ( ti @ SV90 @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1551 ) @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1552 ) @ SY1551 ) ) )
| ~ ~ ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) )
| ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(856,plain,
! [SV91: $i] :
( ( ! [SY1557: $i,SY1558: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1558 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1557 ) @ SV91 ) ) @ SY1558 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1557 ) ) @ SY1558 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(857,plain,
! [SV91: $i] :
( ( ! [SY1559: $i,SY1560: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY1560 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SY1559 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SY1559 ) ) @ SY1560 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1559 ) @ SV91 ) ) @ SY1560 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(858,plain,
! [SV92: $i] :
( ( ( ~ ! [SY1561: $i] :
( ( ( ti @ SV92 @ SY1561 )
= ( top_top @ SV92 ) )
| ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1561 ) @ ( top_top @ SV92 ) ) ) )
| ~ ! [SY1562: $i] :
( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1562 ) @ ( top_top @ SV92 ) ) )
| ( ( ti @ SV92 @ SY1562 )
!= ( top_top @ SV92 ) ) ) )
= $false )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(859,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(860,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(861,plain,
! [SV264: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SV264 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(862,plain,
! [SV265: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
| ! [SY2069: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2069 ) @ arrow_1834574746e_Prof ) )
| ! [SY2070: $i,SY2071: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2070 ) @ SY2071 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2069 @ ( sK14_I @ SY2071 @ SY2070 @ SY2069 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2070 ) @ SY2071 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SY2069 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(863,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(864,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(865,plain,
! [SV93: $i] :
( ( ( ~ ! [SY1563: $i,SY1564: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1563 ) @ SY1564 ) )
| ( ( ti @ SV93 @ SY1564 )
!= ( ti @ SV93 @ SY1563 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1564 ) @ SY1563 ) ) )
| ~ ! [SY1565: $i,SY1566: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1565 ) @ SY1566 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1566 ) @ SY1565 ) )
| ( ( ti @ SV93 @ SY1566 )
= ( ti @ SV93 @ SY1565 ) ) ) )
= $false )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(866,plain,
! [SV94: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SV166 @ SV94 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(867,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i] :
( ( ~ ( ~ ! [SY2072: $i,SY2073: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SY2073 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2073 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
| ~ ! [SY2074: $i,SY2075: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SY2075 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2075 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(868,plain,
! [SV267: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(869,plain,
! [SV268: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
| ! [SY2078: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2078 ) @ arrow_1834574746e_Prof ) )
| ! [SY2079: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2079 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SY2080: $i,SY2081: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2078 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2079 ) ) ) )
| ~ ! [SY2082: $i,SY2083: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2079 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2078 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(870,plain,
! [SV269: $i] :
( ( ~ ( hBOOL @ ( ti @ bool @ SV269 ) )
| ( hBOOL @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(871,plain,
! [SV270: $i] :
( ( ~ ( hBOOL @ SV270 )
| ( hBOOL @ ( ti @ bool @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(872,plain,
! [SV96: $i,SV168: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV96 ) @ SV168 ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(873,plain,
! [SV97: $i] :
( ( ( ~ ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) )
| ~ ! [SY1580: $i,SY1581: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1580 ) @ SY1581 ) )
| ( ( ti @ SV97 @ SY1580 )
= ( ti @ SV97 @ SY1581 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1581 ) @ SY1580 ) ) ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(874,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(875,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(876,plain,
! [SV214: $i,SV169: $i,SV98: $i] :
( ( ~ ! [SY1953: $i,SY1954: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1954 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1954 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SY1954 @ SY1953 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SY1953 ) ) )
| ~ ! [SY1955: $i,SY1956: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1956 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SY1955 ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1956 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SY1956 @ SY1955 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(877,plain,
! [SV99: $i,SV170: $i,SV215: $i] :
( ( ~ ! [SY1957: $i,SY1958: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SY1958 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1958 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
| ~ ! [SY1959: $i,SY1960: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SY1960 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1960 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(878,plain,
! [SV100: $i] :
( ( ! [SY1594: $i,SY1595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1594 ) @ SY1595 ) )
| ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1595 @ SY1594 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(879,plain,
! [SV100: $i] :
( ( ! [SY1596: $i,SY1597: $i] :
( ~ ( hBOOL @ ( hAPP @ SV100 @ bool @ SY1597 @ SY1596 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SY1596 ) @ SY1597 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(880,plain,
! [SV101: $i] :
( ( ! [SY1598: $i,SY1599: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( sK26_X1 @ SY1599 @ SY1598 @ SV101 ) ) )
| ! [SY1600: $i,SY1601: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1598 ) @ bool @ SY1599 @ ( hAPP @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) @ ( hAPP @ SV101 @ ( fun @ SY1598 @ ( product_prod @ SV101 @ SY1598 ) ) @ ( product_Pair @ SV101 @ SY1598 ) @ SY1600 ) @ SY1601 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(881,plain,
! [SV101: $i] :
( ( ! [SY1602: $i,SY1603: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ ( hAPP @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) @ ( hAPP @ SV101 @ ( fun @ SY1602 @ ( product_prod @ SV101 @ SY1602 ) ) @ ( product_Pair @ SV101 @ SY1602 ) @ ( sK24_A_2 @ SY1603 @ SY1602 @ SV101 ) ) @ ( sK25_SY1332 @ SY1603 @ SY1602 @ SV101 ) ) ) )
| ! [SY1604: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SY1602 ) @ bool @ SY1603 @ SY1604 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(882,plain,
! [SV271: $i,SV102: $i,SV216: $i,SV171: $i] :
( ( ~ ( ~ ! [SY2084: $i,SY2085: $i] :
( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SY2084 ) )
| ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SY2085 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2084 ) @ SY2085 ) ) )
| ~ ~ ( ~ ! [SY2086: $i] :
( ! [SY2087: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2086 ) @ SY2087 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY2086 ) ) )
| ~ ! [SY2088: $i,SY2089: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2088 ) @ SY2089 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2089 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(883,plain,
! [SV217: $i,SV272: $i,SV172: $i,SV103: $i] :
( ( ~ ( ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2090 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2091 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2090 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SY2090 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
| ~ ! [SY2092: $i,SY2093: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2092 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2093 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2092 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SY2092 @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(884,plain,
! [SV218: $i,SV173: $i,SV104: $i] :
( ( ( ~ ( ( ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) )
| ~ ( ( ( ti @ SV104 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( ti @ SV104 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(885,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(886,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(887,plain,
! [SV174: $i,SV105: $i] :
( ( ~ ! [SY1835: $i,SY1836: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1836 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1835 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(888,plain,
! [SV174: $i,SV105: $i] :
( ( ~ ! [SY1837: $i,SY1838: $i] :
( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1838 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1837 ) )
| ~ ( ~ ! [SY1839: $i,SY1840: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1838 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1837 ) ) )
| ~ ! [SY1841: $i,SY1842: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1837 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1838 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(889,plain,
! [SV175: $i,SV106: $i] :
( ( ~ ! [SY1843: $i,SY1844: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1843 ) @ SY1844 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(890,plain,
! [SV175: $i,SV106: $i] :
( ( ~ ! [SY1845: $i,SY1846: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1845 ) @ SY1846 ) )
| ! [SY1847: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1847 ) @ SY1846 ) )
| ! [SY1848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1848 ) @ SY1846 ) )
| ( ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1847 )
!= ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1848 ) )
| ( ( ti @ SV106 @ SY1847 )
= ( ti @ SV106 @ SY1848 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(891,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
| ~ ~ ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(892,plain,
! [SV108: $i,SV177: $i] :
( ( ~ ! [SY1886: $i,SY1887: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1886 )
= ( ti @ arrow_1212486748le_alt @ SY1887 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(893,plain,
! [SV108: $i,SV177: $i] :
( ( ~ ! [SY1888: $i,SY1889: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1888 )
= ( ti @ arrow_1212486748le_alt @ SY1889 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(894,plain,
! [SV109: $i,SV178: $i,SV273: $i,SV220: $i] :
( ( ! [SY2094: $i,SY2095: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2094 )
= ( ti @ arrow_1212486748le_alt @ SY2095 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2094 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2095 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2094 ) @ SY2095 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY2095 @ SY2094 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY2095 @ SY2094 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2094 ) @ SY2095 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY2095 @ SY2094 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY2095 @ SY2094 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2094 ) @ SY2095 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(895,plain,
! [SV274: $i] :
( ( ! [SY2096: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SY2096 @ SV274 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV274 @ ( sK1_X_1 @ SY2096 @ SV274 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SY2096 @ SV274 ) @ SY2096 ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SY2096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(896,plain,
! [SV275: $i] :
( ( ! [SY2097: $i] :
( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV275 ) @ SY2097 ) )
| ! [SY2098: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2098 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV275 @ SY2098 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2098 @ SY2097 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(897,plain,
! [SV276: $i,SV224: $i,SV186: $i,SV125: $i,SV24: $i] :
( ( ! [SY2099: $i] :
( ( hAPP @ ( product_prod @ SV24 @ SV125 ) @ SV186 @ ( hAPP @ ( fun @ SV24 @ ( fun @ SV125 @ SV186 ) ) @ ( fun @ ( product_prod @ SV24 @ SV125 ) @ SV186 ) @ ( product_prod_rec @ SV24 @ SV125 @ SV186 ) @ SV224 ) @ ( hAPP @ SV125 @ ( product_prod @ SV24 @ SV125 ) @ ( hAPP @ SV24 @ ( fun @ SV125 @ ( product_prod @ SV24 @ SV125 ) ) @ ( product_Pair @ SV24 @ SV125 ) @ SV276 ) @ SY2099 ) )
= ( hAPP @ SV125 @ SV186 @ ( hAPP @ SV24 @ ( fun @ SV125 @ SV186 ) @ SV224 @ SV276 ) @ SY2099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(898,plain,
! [SV277: $i,SV126: $i,SV25: $i] :
( ( ( ( hAPP @ SV25 @ SV126 @ ( top_top @ ( fun @ SV25 @ SV126 ) ) @ SV277 )
= ( top_top @ SV126 ) )
= $true )
| ( ( top @ SV126 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(899,plain,
! [SV225: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ SV26 @ bool @ ( hAPP @ SV26 @ ( fun @ SV26 @ bool ) @ ( ord_less @ SV26 ) @ ( top_top @ SV26 ) ) @ SV225 ) )
= $false )
| ( ( top @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(900,plain,
! [SV278: $i,SV226: $i,SV27: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SV226 ) @ SV278 ) )
| ( ( ti @ SV27 @ SV226 )
= ( ti @ SV27 @ SV278 ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SV278 ) @ SV226 ) ) )
= $true )
| ( ( linorder @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(901,plain,
! [SV279: $i,SV227: $i,SV28: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV227 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV279 ) @ SV227 ) ) )
= $true )
| ( ( preorder @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(902,plain,
! [SV228: $i,SV280: $i,SV29: $i] :
( ( ( ! [SY2100: $i] :
( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV280 ) @ SY2100 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV280 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SY2100 ) ) ) )
= $true )
| ( ( order @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(903,plain,
! [SV229: $i,SV281: $i,SV30: $i] :
( ( ( ! [SY2101: $i] :
( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SY2101 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SY2101 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV229 ) ) ) )
= $true )
| ( ( preorder @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(904,plain,
! [SV230: $i,SV282: $i,SV31: $i] :
( ( ( ! [SY2102: $i] :
( ~ ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV282 ) @ SY2102 ) )
| ( SV282 != SV230 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV230 ) @ SY2102 ) ) ) )
= $true )
| ( ( order @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(905,plain,
! [SV231: $i,SV283: $i,SV32: $i] :
( ( ( ! [SY2103: $i] :
( ~ ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SY2103 ) )
| ( SY2103 != SV231 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV231 ) ) ) )
= $true )
| ( ( ord @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(906,plain,
! [SV232: $i,SV33: $i,SV284: $i] :
( ( ( ! [SY2104: $i] :
( ( SV284 != SY2104 )
| ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SY2104 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV284 ) ) ) )
= $true )
| ( ( order @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(907,plain,
! [SV233: $i,SV34: $i,SV285: $i] :
( ( ( ! [SY2105: $i] :
( ( SV285 != SY2105 )
| ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SY2105 ) @ SV233 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV285 ) @ SV233 ) ) ) )
= $true )
| ( ( ord @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(908,plain,
! [SV286: $i,SV234: $i,SV35: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV234 ) @ SV286 ) )
| ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV286 ) @ SV234 ) ) )
= $true )
| ( ( order @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(909,plain,
! [SV287: $i,SV235: $i,SV36: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV235 ) @ SV287 ) )
| ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV287 ) @ SV235 ) ) )
= $true )
| ( ( preorder @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(910,plain,
! [SV236: $i,SV288: $i,SV37: $i] :
( ( ( ! [SY2106: $i] :
( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV288 ) @ SY2106 ) )
| ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SY2106 ) @ SV288 ) )
| ( hBOOL @ SV236 ) ) )
= $true )
| ( ( preorder @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(911,plain,
! [SV289: $i,SV237: $i,SV38: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SV237 ) @ SV289 ) )
| ( SV289 != SV237 ) )
= $true )
| ( ( order @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(912,plain,
! [SV290: $i,SV238: $i,SV39: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SV238 ) @ SV290 ) )
| ( SV238 != SV290 ) )
= $true )
| ( ( order @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(913,plain,
! [SV291: $i,SV239: $i,SV40: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV239 ) @ SV291 ) )
| ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV291 ) @ SV239 ) ) )
= $true )
| ( ( preorder @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(914,plain,
! [SV292: $i,SV240: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV240 ) @ SV292 ) )
| ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV292 ) @ SV240 ) ) )
= $true )
| ( ( preorder @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(915,plain,
! [SV293: $i,SV241: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SV241 ) @ SV293 ) )
| ( SV241 != SV293 ) )
= $true )
| ( ( order @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(916,plain,
! [SV294: $i,SV242: $i,SV43: $i] :
( ( ( ( ( ti @ SV43 @ SV242 )
= ( ti @ SV43 @ SV294 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SV242 ) @ SV294 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SV294 ) @ SV242 ) ) )
= $true )
| ( ( linorder @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(917,plain,
! [SV243: $i,SV295: $i,SV44: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SV295 ) @ SV243 ) )
| ( ( ti @ SV44 @ SV243 )
= ( ti @ SV44 @ SV295 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SV243 ) @ SV295 ) ) )
= $true )
| ( ( linorder @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(918,plain,
! [SV244: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ SV45 @ bool @ ( hAPP @ SV45 @ ( fun @ SV45 @ bool ) @ ( ord_less @ SV45 ) @ SV244 ) @ SV244 ) )
= $false )
| ( ( preorder @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(919,plain,
! [SV245: $i,SV187: $i,SV296: $i,SV127: $i,SV47: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SV296 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
| ( ( hAPP @ SV47 @ SV127 @ SV296 @ SV187 )
!= ( ti @ SV127 @ SV245 ) )
| ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SV296 ) @ SV245 )
= ( ti @ SV47 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(920,plain,
! [SV188: $i,SV246: $i,SV128: $i,SV48: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV48 @ bool ) @ bool @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ ( fun @ SV48 @ bool ) @ bool ) @ ( inj_on @ SV48 @ SV128 ) @ SV246 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) ) )
= $true )
| ( ( ( hAPP @ SV128 @ SV48 @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) @ ( hAPP @ ( fun @ SV48 @ bool ) @ ( fun @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) ) @ ( hilbert_inv_into @ SV48 @ SV128 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) @ SV246 ) @ ( hAPP @ SV48 @ SV128 @ SV246 @ SV188 ) )
= ( ti @ SV48 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(921,plain,
! [SV49: $i,SV247: $i,SV189: $i,SV129: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ SV189 ) @ SV247 ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV189 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) ) @ ( combb @ SV189 @ ( fun @ SV49 @ SV189 ) @ SV129 ) @ ( combk @ SV189 @ SV49 ) ) @ SV247 ) ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(922,plain,
! [SV190: $i,SV297: $i,SV248: $i,SV130: $i,SV50: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SV248 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SV190 ) @ SV297 ) )
| ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SV297 ) @ SV248 ) @ ( hAPP @ SV50 @ SV130 @ SV248 @ SV190 ) )
= ( ti @ SV50 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(923,plain,
! [SV191: $i,SV249: $i,SV298: $i,SV131: $i,SV51: $i] :
( ( ! [SY2107: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SY2107 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SY2107 ) )
| ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SY2107 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(924,plain,
! [SV250: $i,SV192: $i,SV299: $i,SV132: $i,SV52: $i] :
( ( ! [SY2108: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SY2108 ) )
| ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SY2108 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SY2108 ) )
| ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(925,plain,
! [SV251: $i,SV193: $i,SV300: $i,SV133: $i,SV53: $i] :
( ( ! [SY2109: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SY2109 ) )
| ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
!= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SY2109 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SY2109 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(926,plain,
! [SV252: $i,SV194: $i,SV301: $i,SV135: $i,SV55: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SV301 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
| ( ( hAPP @ SV55 @ SV135 @ SV301 @ SV194 )
!= ( hAPP @ SV55 @ SV135 @ SV301 @ SV252 ) )
| ( ( ti @ SV55 @ SV194 )
= ( ti @ SV55 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(927,plain,
! [SV195: $i,SV253: $i,SV136: $i,SV56: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SV136 ) @ SV253 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) ) )
= $true )
| ( ( ( ( hAPP @ SV56 @ SV136 @ SV253 @ ( hAPP @ SV136 @ SV56 @ SV195 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
!= ( ti @ SV136 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
| ( ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SV136 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SV253 )
= ( ti @ ( fun @ SV136 @ SV56 ) @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(928,plain,
! [SV137: $i,SV57: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV196 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SV137 ) ) @ SV196 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV137 ) @ SV57 ) ) @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(929,plain,
! [SV254: $i,SV197: $i,SV138: $i,SV58: $i] :
( ( ( ( ( hAPP @ SV58 @ SV138 @ SV197 @ ( sK6_X_1 @ SV254 @ SV197 @ SV138 @ SV58 ) )
!= ( hAPP @ SV58 @ SV138 @ SV254 @ ( sK6_X_1 @ SV254 @ SV197 @ SV138 @ SV58 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ SV58 @ SV138 ) @ SV197 )
= ( ti @ ( fun @ SV58 @ SV138 ) @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(930,plain,
! [SV198: $i,SV142: $i,SV62: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV62 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV62 ) @ SV142 ) @ SV198 ) ) @ arrow_638930832le_Lin ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV142 )
= ( ti @ arrow_1212486748le_alt @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(931,plain,
! [SV199: $i,SV302: $i,SV255: $i,SV143: $i,SV64: $i] :
( ( ! [SY2110: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SV255 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SV302 ) @ SY2110 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SV255 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SY2110 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(932,plain,
! [SV200: $i,SV303: $i,SV256: $i,SV144: $i,SV66: $i] :
( ( ! [SY2111: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SV256 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SV303 ) @ SY2111 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SV256 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SY2111 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(933,plain,
! [SV201: $i,SV304: $i,SV257: $i,SV145: $i,SV67: $i] :
( ( ! [SY2112: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SV257 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SV304 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SY2112 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SV304 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SV257 @ SV201 ) ) @ SY2112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(934,plain,
! [SV305: $i,SV258: $i,SV205: $i,SV155: $i,SV78: $i] :
( ( ! [SY2113: $i] :
( ( hAPP @ SV78 @ SV155 @ ( hAPP @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) @ ( hAPP @ ( fun @ SV205 @ SV155 ) @ ( fun @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) ) @ ( combb @ SV205 @ SV155 @ SV78 ) @ SV258 ) @ SV305 ) @ SY2113 )
= ( hAPP @ SV205 @ SV155 @ SV258 @ ( hAPP @ SV78 @ SV205 @ SV305 @ SY2113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(935,plain,
! [SV306: $i,SV259: $i,SV206: $i,SV156: $i,SV79: $i] :
( ( ! [SY2114: $i] :
( ( hAPP @ SV79 @ SV156 @ ( hAPP @ SV206 @ ( fun @ SV79 @ SV156 ) @ ( hAPP @ ( fun @ SV79 @ ( fun @ SV206 @ SV156 ) ) @ ( fun @ SV206 @ ( fun @ SV79 @ SV156 ) ) @ ( combc @ SV79 @ SV206 @ SV156 ) @ SV259 ) @ SV306 ) @ SY2114 )
= ( hAPP @ SV206 @ SV156 @ ( hAPP @ SV79 @ ( fun @ SV206 @ SV156 ) @ SV259 @ SY2114 ) @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(936,plain,
! [SV307: $i,SV261: $i,SV208: $i,SV159: $i,SV82: $i] :
( ( ! [SY2115: $i] :
( ( hAPP @ SV82 @ SV159 @ ( hAPP @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) @ ( hAPP @ ( fun @ SV82 @ ( fun @ SV208 @ SV159 ) ) @ ( fun @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) ) @ ( combs @ SV82 @ SV208 @ SV159 ) @ SV261 ) @ SV307 ) @ SY2115 )
= ( hAPP @ SV208 @ SV159 @ ( hAPP @ SV82 @ ( fun @ SV208 @ SV159 ) @ SV261 @ SY2115 ) @ ( hAPP @ SV82 @ SV208 @ SV307 @ SY2115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(937,plain,
! [SV209: $i,SV160: $i,SV84: $i] :
( ( ( hBOOL @ ( hAPP @ SV84 @ bool @ ( hAPP @ SV84 @ ( fun @ SV84 @ bool ) @ ( fequal @ SV84 ) @ SV160 ) @ SV209 ) )
= $false )
| ( ( ( ti @ SV84 @ SV160 )
= ( ti @ SV84 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(938,plain,
! [SV210: $i,SV161: $i,SV85: $i] :
( ( ( ( ti @ SV85 @ SV161 )
= ( ti @ SV85 @ SV210 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV85 @ bool @ ( hAPP @ SV85 @ ( fun @ SV85 @ bool ) @ ( fequal @ SV85 ) @ SV161 ) @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(939,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
| ~ ~ ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(940,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
| ~ ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1776 ) @ SY1777 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1777 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1776 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(941,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ~ ! [SY2060: $i,SY2061: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2060 )
= ( ti @ arrow_1212486748le_alt @ SY2061 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
| ~ ! [SY2062: $i,SY2063: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2062 )
= ( ti @ arrow_1212486748le_alt @ SY2063 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(942,plain,
! [SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ~ ! [SY2064: $i] :
( ! [SY2065: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2064 ) @ SY2065 ) )
| ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SY2064 ) ) )
| ~ ! [SY2066: $i,SY2067: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2066 ) @ SY2067 ) )
| ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SY2067 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(943,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
| ~ ~ ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(944,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
| ~ ! [SY1802: $i,SY1803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1802 ) @ SY1803 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1803 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1802 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(945,plain,
! [SV90: $i] :
( ( ( ~ ! [SY1551: $i,SY1552: $i] :
( ( ( ti @ SV90 @ SY1551 )
= ( ti @ SV90 @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1551 ) @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1552 ) @ SY1551 ) ) ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(946,plain,
! [SV90: $i] :
( ( ( ~ ~ ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) )
| ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(947,plain,
! [SV308: $i,SV91: $i] :
( ( ! [SY2116: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY2116 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SY2116 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SY2116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(948,plain,
! [SV309: $i,SV91: $i] :
( ( ! [SY2117: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SY2117 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV309 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV309 ) ) @ SY2117 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV309 ) @ SV91 ) ) @ SY2117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(949,plain,
! [SV92: $i] :
( ( ( ~ ! [SY1561: $i] :
( ( ( ti @ SV92 @ SY1561 )
= ( top_top @ SV92 ) )
| ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1561 ) @ ( top_top @ SV92 ) ) ) ) )
= $false )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(950,plain,
! [SV92: $i] :
( ( ( ~ ! [SY1562: $i] :
( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1562 ) @ ( top_top @ SV92 ) ) )
| ( ( ti @ SV92 @ SY1562 )
!= ( top_top @ SV92 ) ) ) )
= $false )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(951,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(952,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ p ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(953,plain,
! [SV264: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SV264 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(954,plain,
! [SV265: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) ) )
= $true )
| ( ( ! [SY2069: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2069 ) @ arrow_1834574746e_Prof ) )
| ! [SY2070: $i,SY2071: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2070 ) @ SY2071 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2069 @ ( sK14_I @ SY2071 @ SY2070 @ SY2069 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2070 ) @ SY2071 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SY2069 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(955,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(956,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(957,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(958,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(959,plain,
! [SV93: $i] :
( ( ( ~ ! [SY1563: $i,SY1564: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1563 ) @ SY1564 ) )
| ( ( ti @ SV93 @ SY1564 )
!= ( ti @ SV93 @ SY1563 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1564 ) @ SY1563 ) ) ) )
= $false )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(960,plain,
! [SV93: $i] :
( ( ( ~ ! [SY1565: $i,SY1566: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1565 ) @ SY1566 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1566 ) @ SY1565 ) )
| ( ( ti @ SV93 @ SY1566 )
= ( ti @ SV93 @ SY1565 ) ) ) )
= $false )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(961,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SV166 @ SV94 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(962,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i] :
( ( ~ ! [SY2072: $i,SY2073: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SY2073 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2073 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
| ~ ! [SY2074: $i,SY2075: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SY2075 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2075 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(963,plain,
! [SV267: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(964,plain,
! [SV268: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) ) )
= $true )
| ( ( ! [SY2078: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2078 ) @ arrow_1834574746e_Prof ) )
| ! [SY2079: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2079 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SY2080: $i,SY2081: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2078 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2079 ) ) ) )
| ~ ! [SY2082: $i,SY2083: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2079 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2078 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(965,plain,
! [SV269: $i] :
( ( ( ~ ( hBOOL @ ( ti @ bool @ SV269 ) ) )
= $true )
| ( ( hBOOL @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(966,plain,
! [SV270: $i] :
( ( ( ~ ( hBOOL @ SV270 ) )
= $true )
| ( ( hBOOL @ ( ti @ bool @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(967,plain,
! [SV96: $i,SV168: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) @ arrow_638930832le_Lin ) ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SV168 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(968,plain,
! [SV168: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV96 ) @ SV168 ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SV168 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(969,plain,
! [SV97: $i] :
( ( ( ~ ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(970,plain,
! [SV97: $i] :
( ( ( ~ ! [SY1580: $i,SY1581: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1580 ) @ SY1581 ) )
| ( ( ti @ SV97 @ SY1580 )
= ( ti @ SV97 @ SY1581 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1581 ) @ SY1580 ) ) ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(971,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(972,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ lab ) ) @ lba ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( ord_less @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_992993526_mktop ) @ p ) ) @ e ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combs @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ bool @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ ( if @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ arrow_1384031255e_indi @ bool ) ) @ ( combc @ arrow_1384031255e_indi @ nat @ bool ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ nat ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ nat @ bool ) ) ) @ ( combb @ nat @ ( fun @ nat @ bool ) @ arrow_1384031255e_indi ) @ ( fequal @ nat ) ) @ h ) ) @ n ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1384031255e_indi ) @ arrow_1726925404_above ) @ p ) ) @ c ) ) @ e ) ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( combc @ arrow_1384031255e_indi @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1384031255e_indi ) @ arrow_844286440_mkbot ) @ p ) ) @ e ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(973,plain,
! [SV214: $i,SV169: $i,SV98: $i] :
( ( ~ ! [SY1953: $i,SY1954: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1954 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1954 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SY1954 @ SY1953 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SY1953 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(974,plain,
! [SV214: $i,SV169: $i,SV98: $i] :
( ( ~ ! [SY1955: $i,SY1956: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1956 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SY1955 ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1956 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SY1956 @ SY1955 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(975,plain,
! [SV99: $i,SV170: $i,SV215: $i] :
( ( ~ ! [SY1957: $i,SY1958: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SY1958 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1958 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(976,plain,
! [SV99: $i,SV170: $i,SV215: $i] :
( ( ~ ! [SY1959: $i,SY1960: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SY1960 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1960 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(977,plain,
! [SV310: $i,SV100: $i] :
( ( ! [SY2118: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV310 ) @ SY2118 ) )
| ( hBOOL @ ( hAPP @ SV100 @ bool @ SY2118 @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(978,plain,
! [SV311: $i,SV100: $i] :
( ( ! [SY2119: $i] :
( ~ ( hBOOL @ ( hAPP @ SV100 @ bool @ SY2119 @ SV311 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV311 ) @ SY2119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(979,plain,
! [SV312: $i,SV101: $i] :
( ( ! [SY2120: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SY2120 @ ( sK26_X1 @ SY2120 @ SV312 @ SV101 ) ) )
| ! [SY2121: $i,SY2122: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SY2120 @ ( hAPP @ SV312 @ ( product_prod @ SV101 @ SV312 ) @ ( hAPP @ SV101 @ ( fun @ SV312 @ ( product_prod @ SV101 @ SV312 ) ) @ ( product_Pair @ SV101 @ SV312 ) @ SY2121 ) @ SY2122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(980,plain,
! [SV313: $i,SV101: $i] :
( ( ! [SY2123: $i] :
( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SY2123 @ ( hAPP @ SV313 @ ( product_prod @ SV101 @ SV313 ) @ ( hAPP @ SV101 @ ( fun @ SV313 @ ( product_prod @ SV101 @ SV313 ) ) @ ( product_Pair @ SV101 @ SV313 ) @ ( sK24_A_2 @ SY2123 @ SV313 @ SV101 ) ) @ ( sK25_SY1332 @ SY2123 @ SV313 @ SV101 ) ) ) )
| ! [SY2124: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SY2123 @ SY2124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(981,plain,
! [SV271: $i,SV102: $i,SV216: $i,SV171: $i] :
( ( ~ ! [SY2084: $i,SY2085: $i] :
( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SY2084 ) )
| ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SY2085 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2084 ) @ SY2085 ) ) )
| ~ ~ ( ~ ! [SY2086: $i] :
( ! [SY2087: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2086 ) @ SY2087 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY2086 ) ) )
| ~ ! [SY2088: $i,SY2089: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2088 ) @ SY2089 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2089 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(982,plain,
! [SV217: $i,SV272: $i,SV172: $i,SV103: $i] :
( ( ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2090 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2091 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2090 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SY2090 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
| ~ ! [SY2092: $i,SY2093: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2092 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2093 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2092 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SY2092 @ SV217 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(983,plain,
! [SV218: $i,SV173: $i,SV104: $i] :
( ( ( ( ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) )
| ~ ( ( ( ti @ SV104 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( ti @ SV104 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(984,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(985,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[885]) ).
thf(986,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(987,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(988,plain,
! [SV174: $i,SV105: $i] :
( ( ! [SY1835: $i,SY1836: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1836 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY1836 @ SY1835 @ SV174 @ SV105 ) ) ) @ SY1835 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1836 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1835 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(989,plain,
! [SV174: $i,SV105: $i] :
( ( ! [SY1837: $i,SY1838: $i] :
( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1838 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY1837 ) )
| ~ ( ~ ! [SY1839: $i,SY1840: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1838 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1839 ) @ SY1840 ) ) @ SY1837 ) ) )
| ~ ! [SY1841: $i,SY1842: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1837 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY1841 ) @ SY1842 ) ) @ SY1838 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(990,plain,
! [SV175: $i,SV106: $i] :
( ( ! [SY1843: $i,SY1844: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) @ SY1844 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SY1843 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SY1844 @ SY1843 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SY1844 @ SY1843 @ SV175 @ SV106 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1843 ) @ SY1844 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(991,plain,
! [SV175: $i,SV106: $i] :
( ( ! [SY1845: $i,SY1846: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SY1845 ) @ SY1846 ) )
| ! [SY1847: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1847 ) @ SY1846 ) )
| ! [SY1848: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY1848 ) @ SY1846 ) )
| ( ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1847 )
!= ( hAPP @ SV106 @ SV175 @ SY1845 @ SY1848 ) )
| ( ( ti @ SV106 @ SY1847 )
= ( ti @ SV106 @ SY1848 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[890]) ).
thf(992,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(993,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
| ~ ~ ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(994,plain,
! [SV108: $i,SV177: $i] :
( ( ! [SY1886: $i,SY1887: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1886 )
= ( ti @ arrow_1212486748le_alt @ SY1887 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY1887 @ SY1886 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1886 ) @ SY1887 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1887 ) @ SY1886 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(995,plain,
! [SV108: $i,SV177: $i] :
( ( ! [SY1888: $i,SY1889: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1888 )
= ( ti @ arrow_1212486748le_alt @ SY1889 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY1889 @ SY1888 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1889 ) @ SY1888 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1888 ) @ SY1889 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(996,plain,
! [SV109: $i,SV178: $i,SV273: $i,SV220: $i,SV314: $i] :
( ( ! [SY2125: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SY2125 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2125 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SY2125 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY2125 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY2125 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SY2125 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SY2125 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SY2125 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SY2125 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(997,plain,
! [SV274: $i,SV315: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SV315 @ SV274 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV274 @ ( sK1_X_1 @ SV315 @ SV274 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SV315 @ SV274 ) @ SV315 ) ) ) )
| ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(998,plain,
! [SV316: $i,SV275: $i] :
( ( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV275 ) @ SV316 ) )
| ! [SY2126: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2126 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV275 @ SY2126 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2126 @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(999,plain,
! [SV317: $i,SV276: $i,SV224: $i,SV186: $i,SV125: $i,SV24: $i] :
( ( ( hAPP @ ( product_prod @ SV24 @ SV125 ) @ SV186 @ ( hAPP @ ( fun @ SV24 @ ( fun @ SV125 @ SV186 ) ) @ ( fun @ ( product_prod @ SV24 @ SV125 ) @ SV186 ) @ ( product_prod_rec @ SV24 @ SV125 @ SV186 ) @ SV224 ) @ ( hAPP @ SV125 @ ( product_prod @ SV24 @ SV125 ) @ ( hAPP @ SV24 @ ( fun @ SV125 @ ( product_prod @ SV24 @ SV125 ) ) @ ( product_Pair @ SV24 @ SV125 ) @ SV276 ) @ SV317 ) )
= ( hAPP @ SV125 @ SV186 @ ( hAPP @ SV24 @ ( fun @ SV125 @ SV186 ) @ SV224 @ SV276 ) @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1000,plain,
! [SV278: $i,SV226: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SV226 ) @ SV278 ) )
= $true )
| ( ( ( ( ti @ SV27 @ SV226 )
= ( ti @ SV27 @ SV278 ) )
| ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SV278 ) @ SV226 ) ) )
= $true )
| ( ( linorder @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1001,plain,
! [SV279: $i,SV227: $i,SV28: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV227 ) @ SV279 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV279 ) @ SV227 ) ) )
= $true )
| ( ( preorder @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1002,plain,
! [SV228: $i,SV318: $i,SV280: $i,SV29: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV280 ) @ SV318 ) )
| ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV280 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV318 ) ) )
= $true )
| ( ( order @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1003,plain,
! [SV229: $i,SV319: $i,SV281: $i,SV30: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV319 ) )
| ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV319 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV229 ) ) )
= $true )
| ( ( preorder @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1004,plain,
! [SV230: $i,SV320: $i,SV282: $i,SV31: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV282 ) @ SV320 ) )
| ( SV282 != SV230 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV230 ) @ SV320 ) ) )
= $true )
| ( ( order @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1005,plain,
! [SV231: $i,SV321: $i,SV283: $i,SV32: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV321 ) )
| ( SV321 != SV231 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV231 ) ) )
= $true )
| ( ( ord @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1006,plain,
! [SV232: $i,SV33: $i,SV322: $i,SV284: $i] :
( ( ( ( SV284 != SV322 )
| ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV284 ) ) )
= $true )
| ( ( order @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1007,plain,
! [SV233: $i,SV34: $i,SV323: $i,SV285: $i] :
( ( ( ( SV285 != SV323 )
| ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV323 ) @ SV233 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV285 ) @ SV233 ) ) )
= $true )
| ( ( ord @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1008,plain,
! [SV286: $i,SV234: $i,SV35: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV234 ) @ SV286 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV286 ) @ SV234 ) ) )
= $true )
| ( ( order @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1009,plain,
! [SV287: $i,SV235: $i,SV36: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV235 ) @ SV287 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV287 ) @ SV235 ) ) )
= $true )
| ( ( preorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(1010,plain,
! [SV236: $i,SV324: $i,SV288: $i,SV37: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV288 ) @ SV324 ) )
| ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV324 ) @ SV288 ) )
| ( hBOOL @ SV236 ) )
= $true )
| ( ( preorder @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1011,plain,
! [SV289: $i,SV237: $i,SV38: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SV237 ) @ SV289 ) ) )
= $true )
| ( ( ( SV289 != SV237 ) )
= $true )
| ( ( order @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1012,plain,
! [SV290: $i,SV238: $i,SV39: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SV238 ) @ SV290 ) ) )
= $true )
| ( ( ( SV238 != SV290 ) )
= $true )
| ( ( order @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1013,plain,
! [SV291: $i,SV239: $i,SV40: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV239 ) @ SV291 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV291 ) @ SV239 ) ) )
= $true )
| ( ( preorder @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1014,plain,
! [SV292: $i,SV240: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV240 ) @ SV292 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV292 ) @ SV240 ) ) )
= $true )
| ( ( preorder @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1015,plain,
! [SV293: $i,SV241: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SV241 ) @ SV293 ) ) )
= $true )
| ( ( ( SV241 != SV293 ) )
= $true )
| ( ( order @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1016,plain,
! [SV294: $i,SV242: $i,SV43: $i] :
( ( ( ( ti @ SV43 @ SV242 )
= ( ti @ SV43 @ SV294 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SV242 ) @ SV294 ) )
| ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SV294 ) @ SV242 ) ) )
= $true )
| ( ( linorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1017,plain,
! [SV243: $i,SV295: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SV295 ) @ SV243 ) )
= $true )
| ( ( ( ( ti @ SV44 @ SV243 )
= ( ti @ SV44 @ SV295 ) )
| ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SV243 ) @ SV295 ) ) )
= $true )
| ( ( linorder @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1018,plain,
! [SV245: $i,SV187: $i,SV296: $i,SV127: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SV296 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) ) )
= $true )
| ( ( ( ( hAPP @ SV47 @ SV127 @ SV296 @ SV187 )
!= ( ti @ SV127 @ SV245 ) )
| ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SV296 ) @ SV245 )
= ( ti @ SV47 @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1019,plain,
! [SV188: $i,SV246: $i,SV128: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV48 @ bool ) @ bool @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ ( fun @ SV48 @ bool ) @ bool ) @ ( inj_on @ SV48 @ SV128 ) @ SV246 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) )
= $false )
| ( ( ( hAPP @ SV128 @ SV48 @ ( hAPP @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) @ ( hAPP @ ( fun @ SV48 @ bool ) @ ( fun @ ( fun @ SV48 @ SV128 ) @ ( fun @ SV128 @ SV48 ) ) @ ( hilbert_inv_into @ SV48 @ SV128 ) @ ( top_top @ ( fun @ SV48 @ bool ) ) ) @ SV246 ) @ ( hAPP @ SV48 @ SV128 @ SV246 @ SV188 ) )
= ( ti @ SV48 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1020,plain,
! [SV49: $i,SV247: $i,SV189: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ SV189 ) @ SV247 ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV129 @ bool ) @ bool @ ( hAPP @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ bool ) @ bool ) @ ( inj_on @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) @ ( hAPP @ ( fun @ SV189 @ ( fun @ SV49 @ SV189 ) ) @ ( fun @ ( fun @ SV129 @ SV189 ) @ ( fun @ SV129 @ ( fun @ SV49 @ SV189 ) ) ) @ ( combb @ SV189 @ ( fun @ SV49 @ SV189 ) @ SV129 ) @ ( combk @ SV189 @ SV49 ) ) @ SV247 ) ) @ ( top_top @ ( fun @ SV129 @ bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1021,plain,
! [SV190: $i,SV297: $i,SV248: $i,SV130: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SV248 ) @ SV297 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SV190 ) @ SV297 ) )
| ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SV297 ) @ SV248 ) @ ( hAPP @ SV50 @ SV130 @ SV248 @ SV190 ) )
= ( ti @ SV50 @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1022,plain,
! [SV191: $i,SV249: $i,SV325: $i,SV298: $i,SV131: $i,SV51: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SV325 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SV325 ) )
| ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SV325 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1023,plain,
! [SV250: $i,SV192: $i,SV326: $i,SV299: $i,SV132: $i,SV52: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
| ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
| ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1024,plain,
! [SV251: $i,SV193: $i,SV327: $i,SV300: $i,SV133: $i,SV53: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
| ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
!= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1025,plain,
! [SV252: $i,SV194: $i,SV301: $i,SV135: $i,SV55: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SV301 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) ) )
= $true )
| ( ( ( ( hAPP @ SV55 @ SV135 @ SV301 @ SV194 )
!= ( hAPP @ SV55 @ SV135 @ SV301 @ SV252 ) )
| ( ( ti @ SV55 @ SV194 )
= ( ti @ SV55 @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1026,plain,
! [SV195: $i,SV253: $i,SV136: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SV136 ) @ SV253 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) )
= $false )
| ( ( ( ( hAPP @ SV56 @ SV136 @ SV253 @ ( hAPP @ SV136 @ SV56 @ SV195 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
!= ( ti @ SV136 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
| ( ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SV136 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SV253 )
= ( ti @ ( fun @ SV136 @ SV56 ) @ SV195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1027,plain,
! [SV196: $i,SV137: $i,SV57: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SV137 ) ) @ SV196 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV137 ) @ SV57 ) ) @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV196 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1028,plain,
! [SV254: $i,SV197: $i,SV138: $i,SV58: $i] :
( ( ( ( hAPP @ SV58 @ SV138 @ SV197 @ ( sK6_X_1 @ SV254 @ SV197 @ SV138 @ SV58 ) )
= ( hAPP @ SV58 @ SV138 @ SV254 @ ( sK6_X_1 @ SV254 @ SV197 @ SV138 @ SV58 ) ) )
= $false )
| ( ( ( ti @ ( fun @ SV58 @ SV138 ) @ SV197 )
= ( ti @ ( fun @ SV58 @ SV138 ) @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1029,plain,
! [SV198: $i,SV142: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV62 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV62 ) @ SV142 ) @ SV198 ) ) @ arrow_638930832le_Lin ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV142 )
= ( ti @ arrow_1212486748le_alt @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1030,plain,
! [SV199: $i,SV328: $i,SV302: $i,SV255: $i,SV143: $i,SV64: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SV255 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SV302 ) @ SV328 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SV255 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SV328 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1031,plain,
! [SV200: $i,SV329: $i,SV303: $i,SV256: $i,SV144: $i,SV66: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SV256 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SV303 ) @ SV329 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SV256 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SV329 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1032,plain,
! [SV201: $i,SV330: $i,SV304: $i,SV257: $i,SV145: $i,SV67: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SV257 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SV304 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SV330 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SV304 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SV257 @ SV201 ) ) @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1033,plain,
! [SV331: $i,SV305: $i,SV258: $i,SV205: $i,SV155: $i,SV78: $i] :
( ( ( hAPP @ SV78 @ SV155 @ ( hAPP @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) @ ( hAPP @ ( fun @ SV205 @ SV155 ) @ ( fun @ ( fun @ SV78 @ SV205 ) @ ( fun @ SV78 @ SV155 ) ) @ ( combb @ SV205 @ SV155 @ SV78 ) @ SV258 ) @ SV305 ) @ SV331 )
= ( hAPP @ SV205 @ SV155 @ SV258 @ ( hAPP @ SV78 @ SV205 @ SV305 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1034,plain,
! [SV332: $i,SV306: $i,SV259: $i,SV206: $i,SV156: $i,SV79: $i] :
( ( ( hAPP @ SV79 @ SV156 @ ( hAPP @ SV206 @ ( fun @ SV79 @ SV156 ) @ ( hAPP @ ( fun @ SV79 @ ( fun @ SV206 @ SV156 ) ) @ ( fun @ SV206 @ ( fun @ SV79 @ SV156 ) ) @ ( combc @ SV79 @ SV206 @ SV156 ) @ SV259 ) @ SV306 ) @ SV332 )
= ( hAPP @ SV206 @ SV156 @ ( hAPP @ SV79 @ ( fun @ SV206 @ SV156 ) @ SV259 @ SV332 ) @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1035,plain,
! [SV333: $i,SV307: $i,SV261: $i,SV208: $i,SV159: $i,SV82: $i] :
( ( ( hAPP @ SV82 @ SV159 @ ( hAPP @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) @ ( hAPP @ ( fun @ SV82 @ ( fun @ SV208 @ SV159 ) ) @ ( fun @ ( fun @ SV82 @ SV208 ) @ ( fun @ SV82 @ SV159 ) ) @ ( combs @ SV82 @ SV208 @ SV159 ) @ SV261 ) @ SV307 ) @ SV333 )
= ( hAPP @ SV208 @ SV159 @ ( hAPP @ SV82 @ ( fun @ SV208 @ SV159 ) @ SV261 @ SV333 ) @ ( hAPP @ SV82 @ SV208 @ SV307 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1036,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
| ~ ~ ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1037,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
| ~ ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1776 ) @ SY1777 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1777 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1776 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1038,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ~ ! [SY2060: $i,SY2061: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2060 )
= ( ti @ arrow_1212486748le_alt @ SY2061 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(1039,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ~ ! [SY2062: $i,SY2063: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2062 )
= ( ti @ arrow_1212486748le_alt @ SY2063 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(1040,plain,
! [SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ~ ! [SY2064: $i] :
( ! [SY2065: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2064 ) @ SY2065 ) )
| ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SY2064 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1041,plain,
! [SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ~ ! [SY2066: $i,SY2067: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2066 ) @ SY2067 ) )
| ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SY2067 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1042,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ~ ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
| ~ ~ ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1043,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ~ ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
| ~ ! [SY1802: $i,SY1803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1802 ) @ SY1803 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1803 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1802 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1044,plain,
! [SV90: $i] :
( ( ( ! [SY1551: $i,SY1552: $i] :
( ( ( ti @ SV90 @ SY1551 )
= ( ti @ SV90 @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1551 ) @ SY1552 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1552 ) @ SY1551 ) ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1045,plain,
! [SV90: $i] :
( ( ( ~ ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) )
| ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1046,plain,
! [SV308: $i,SV91: $i,SV334: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV334 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SV334 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1047,plain,
! [SV309: $i,SV91: $i,SV335: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV335 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV309 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV309 ) ) @ SV335 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV309 ) @ SV91 ) ) @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1048,plain,
! [SV92: $i] :
( ( ( ! [SY1561: $i] :
( ( ( ti @ SV92 @ SY1561 )
= ( top_top @ SV92 ) )
| ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1561 ) @ ( top_top @ SV92 ) ) ) ) )
= $true )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1049,plain,
! [SV92: $i] :
( ( ( ! [SY1562: $i] :
( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SY1562 ) @ ( top_top @ SV92 ) ) )
| ( ( ti @ SV92 @ SY1562 )
!= ( top_top @ SV92 ) ) ) )
= $true )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1050,plain,
! [SV264: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SV264 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1051,plain,
! [SV265: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false )
| ( ( ! [SY2069: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2069 ) @ arrow_1834574746e_Prof ) )
| ! [SY2070: $i,SY2071: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2070 ) @ SY2071 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2069 @ ( sK14_I @ SY2071 @ SY2070 @ SY2069 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2070 ) @ SY2071 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SY2069 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1052,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1053,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1054,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(1055,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(1056,plain,
! [SV93: $i] :
( ( ( ! [SY1563: $i,SY1564: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1563 ) @ SY1564 ) )
| ( ( ti @ SV93 @ SY1564 )
!= ( ti @ SV93 @ SY1563 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1564 ) @ SY1563 ) ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1057,plain,
! [SV93: $i] :
( ( ( ! [SY1565: $i,SY1566: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1565 ) @ SY1566 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY1566 ) @ SY1565 ) )
| ( ( ti @ SV93 @ SY1566 )
= ( ti @ SV93 @ SY1565 ) ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(1058,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SV166 @ SV94 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1059,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i] :
( ( ~ ! [SY2072: $i,SY2073: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SY2073 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2073 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1060,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i] :
( ( ~ ! [SY2074: $i,SY2075: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SY2075 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2075 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1061,plain,
! [SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1062,plain,
! [SV268: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false )
| ( ( ! [SY2078: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2078 ) @ arrow_1834574746e_Prof ) )
| ! [SY2079: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2079 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SY2080: $i,SY2081: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK19_I @ SY2081 @ SY2080 @ SY2079 @ SY2078 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2078 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2080 ) @ SY2081 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2079 ) ) ) )
| ~ ! [SY2082: $i,SY2083: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2078 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2079 @ ( sK18_I @ SY2083 @ SY2082 @ SY2079 @ SY2078 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2079 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2082 ) @ SY2083 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2078 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1063,plain,
! [SV269: $i] :
( ( ( hBOOL @ ( ti @ bool @ SV269 ) )
= $false )
| ( ( hBOOL @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1064,plain,
! [SV270: $i] :
( ( ( hBOOL @ SV270 )
= $false )
| ( ( hBOOL @ ( ti @ bool @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1065,plain,
! [SV96: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) @ arrow_638930832le_Lin ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SV168 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1066,plain,
! [SV168: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV96 ) @ SV168 ) ) @ ( sK2_X_1 @ SV168 @ SV96 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV96 )
= ( ti @ arrow_1212486748le_alt @ SV168 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1067,plain,
! [SV97: $i] :
( ( ( ~ ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1068,plain,
! [SV97: $i] :
( ( ( ! [SY1580: $i,SY1581: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1580 ) @ SY1581 ) )
| ( ( ti @ SV97 @ SY1580 )
= ( ti @ SV97 @ SY1581 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1581 ) @ SY1580 ) ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1069,plain,
! [SV214: $i,SV169: $i,SV98: $i] :
( ( ! [SY1953: $i,SY1954: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1954 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1954 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SY1954 @ SY1953 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SY1953 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1070,plain,
! [SV214: $i,SV169: $i,SV98: $i] :
( ( ! [SY1955: $i,SY1956: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY1956 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SY1955 ) )
| ( ( hAPP @ SV98 @ SV169 @ SY1956 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SY1956 @ SY1955 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1071,plain,
! [SV99: $i,SV170: $i,SV215: $i] :
( ( ! [SY1957: $i,SY1958: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SY1958 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1958 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1957 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY1958 @ SY1957 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1957 ) @ SY1958 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1958 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1072,plain,
! [SV99: $i,SV170: $i,SV215: $i] :
( ( ! [SY1959: $i,SY1960: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SY1960 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1960 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY1959 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY1960 @ SY1959 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1960 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1959 ) @ SY1960 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1073,plain,
! [SV336: $i,SV310: $i,SV100: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV310 ) @ SV336 ) )
| ( hBOOL @ ( hAPP @ SV100 @ bool @ SV336 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1074,plain,
! [SV311: $i,SV337: $i,SV100: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV100 @ bool @ SV337 @ SV311 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV311 ) @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1075,plain,
! [SV338: $i,SV312: $i,SV101: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( sK26_X1 @ SV338 @ SV312 @ SV101 ) ) )
| ! [SY2127: $i,SY2128: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( hAPP @ SV312 @ ( product_prod @ SV101 @ SV312 ) @ ( hAPP @ SV101 @ ( fun @ SV312 @ ( product_prod @ SV101 @ SV312 ) ) @ ( product_Pair @ SV101 @ SV312 ) @ SY2127 ) @ SY2128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1076,plain,
! [SV339: $i,SV313: $i,SV101: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ ( hAPP @ SV313 @ ( product_prod @ SV101 @ SV313 ) @ ( hAPP @ SV101 @ ( fun @ SV313 @ ( product_prod @ SV101 @ SV313 ) ) @ ( product_Pair @ SV101 @ SV313 ) @ ( sK24_A_2 @ SV339 @ SV313 @ SV101 ) ) @ ( sK25_SY1332 @ SV339 @ SV313 @ SV101 ) ) ) )
| ! [SY2129: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ SY2129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1077,plain,
! [SV271: $i,SV102: $i,SV216: $i,SV171: $i] :
( ( ~ ! [SY2084: $i,SY2085: $i] :
( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SY2084 ) )
| ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SY2085 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2084 ) @ SY2085 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1078,plain,
! [SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ~ ~ ( ~ ! [SY2086: $i] :
( ! [SY2087: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2086 ) @ SY2087 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY2086 ) ) )
| ~ ! [SY2088: $i,SY2089: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2088 ) @ SY2089 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2089 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1079,plain,
! [SV217: $i,SV272: $i,SV172: $i,SV103: $i] :
( ( ~ ! [SY2090: $i,SY2091: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2090 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2091 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2090 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SY2090 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1080,plain,
! [SV217: $i,SV272: $i,SV172: $i,SV103: $i] :
( ( ~ ! [SY2092: $i,SY2093: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2092 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2093 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2092 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SY2092 @ SV217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1081,plain,
! [SV218: $i,SV173: $i,SV104: $i] :
( ( ( ( ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1082,plain,
! [SV173: $i,SV218: $i,SV104: $i] :
( ( ( ~ ( ( ( ti @ SV104 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( ti @ SV104 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1083,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1084,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1085,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1086,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1087,plain,
! [SV340: $i,SV174: $i,SV105: $i] :
( ( ! [SY2130: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) ) @ SY2130 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) ) @ SY2130 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SY2130 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY2130 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1088,plain,
! [SV341: $i,SV174: $i,SV105: $i] :
( ( ! [SY2131: $i] :
( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SY2131 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
| ~ ( ~ ! [SY2132: $i,SY2133: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2132 ) @ SY2133 ) ) @ SY2131 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2132 ) @ SY2133 ) ) @ SV341 ) ) )
| ~ ! [SY2134: $i,SY2135: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2134 ) @ SY2135 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2134 ) @ SY2135 ) ) @ SY2131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1089,plain,
! [SV175: $i,SV342: $i,SV106: $i] :
( ( ! [SY2136: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SY2136 @ SV342 @ SV175 @ SV106 ) ) @ SY2136 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SY2136 @ SV342 @ SV175 @ SV106 ) ) @ SY2136 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SY2136 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SY2136 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SY2136 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SY2136 @ SV342 @ SV175 @ SV106 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SY2136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1090,plain,
! [SV343: $i,SV175: $i,SV106: $i] :
( ( ! [SY2137: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SY2137 ) )
| ! [SY2138: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2138 ) @ SY2137 ) )
| ! [SY2139: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2139 ) @ SY2137 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SY2138 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SY2139 ) )
| ( ( ti @ SV106 @ SY2138 )
= ( ti @ SV106 @ SY2139 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1091,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1092,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
| ~ ~ ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1093,plain,
! [SV108: $i,SV177: $i,SV344: $i] :
( ( ! [SY2140: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SY2140 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SY2140 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY2140 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2140 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY2140 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SY2140 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SY2140 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2140 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SY2140 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SY2140 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2140 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1094,plain,
! [SV108: $i,SV177: $i,SV345: $i] :
( ( ! [SY2141: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SY2141 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SY2141 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY2141 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2141 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY2141 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SY2141 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SY2141 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2141 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SY2141 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2141 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SY2141 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1095,plain,
! [SV109: $i,SV178: $i,SV273: $i,SV220: $i,SV346: $i,SV314: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1096,plain,
! [SV274: $i,SV315: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SV315 @ SV274 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV274 @ ( sK1_X_1 @ SV315 @ SV274 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SV315 @ SV274 ) @ SV315 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1097,plain,
! [SV316: $i,SV275: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV275 ) @ SV316 ) ) )
= $true )
| ( ( ! [SY2126: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2126 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV275 @ SY2126 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2126 @ SV316 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1098,plain,
! [SV278: $i,SV226: $i,SV27: $i] :
( ( ( ( ti @ SV27 @ SV226 )
= ( ti @ SV27 @ SV278 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SV278 ) @ SV226 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV27 @ bool @ ( hAPP @ SV27 @ ( fun @ SV27 @ bool ) @ ( ord_less @ SV27 ) @ SV226 ) @ SV278 ) )
= $true )
| ( ( linorder @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1099,plain,
! [SV279: $i,SV227: $i,SV28: $i] :
( ( ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV227 ) @ SV279 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV279 ) @ SV227 ) ) )
= $true )
| ( ( preorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1100,plain,
! [SV228: $i,SV318: $i,SV280: $i,SV29: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV280 ) @ SV318 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV280 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV318 ) ) )
= $true )
| ( ( order @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1101,plain,
! [SV229: $i,SV319: $i,SV281: $i,SV30: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV319 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV319 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV229 ) ) )
= $true )
| ( ( preorder @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1102,plain,
! [SV230: $i,SV320: $i,SV282: $i,SV31: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV282 ) @ SV320 ) ) )
= $true )
| ( ( ( SV282 != SV230 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV230 ) @ SV320 ) ) )
= $true )
| ( ( order @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1103,plain,
! [SV231: $i,SV321: $i,SV283: $i,SV32: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV321 ) ) )
= $true )
| ( ( ( SV321 != SV231 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV231 ) ) )
= $true )
| ( ( ord @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1104,plain,
! [SV232: $i,SV33: $i,SV322: $i,SV284: $i] :
( ( ( ( SV284 != SV322 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV284 ) ) )
= $true )
| ( ( order @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1105,plain,
! [SV233: $i,SV34: $i,SV323: $i,SV285: $i] :
( ( ( ( SV285 != SV323 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV323 ) @ SV233 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV285 ) @ SV233 ) ) )
= $true )
| ( ( ord @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1106,plain,
! [SV286: $i,SV234: $i,SV35: $i] :
( ( ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV234 ) @ SV286 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV286 ) @ SV234 ) ) )
= $true )
| ( ( order @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1107,plain,
! [SV287: $i,SV235: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV235 ) @ SV287 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV287 ) @ SV235 ) ) )
= $true )
| ( ( preorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1108,plain,
! [SV236: $i,SV324: $i,SV288: $i,SV37: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV288 ) @ SV324 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV324 ) @ SV288 ) )
| ( hBOOL @ SV236 ) )
= $true )
| ( ( preorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1109,plain,
! [SV289: $i,SV237: $i,SV38: $i] :
( ( ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SV237 ) @ SV289 ) )
= $false )
| ( ( ( SV289 != SV237 ) )
= $true )
| ( ( order @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1110,plain,
! [SV290: $i,SV238: $i,SV39: $i] :
( ( ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SV238 ) @ SV290 ) )
= $false )
| ( ( ( SV238 != SV290 ) )
= $true )
| ( ( order @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1111,plain,
! [SV291: $i,SV239: $i,SV40: $i] :
( ( ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV239 ) @ SV291 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV291 ) @ SV239 ) ) )
= $true )
| ( ( preorder @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1112,plain,
! [SV292: $i,SV240: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV240 ) @ SV292 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV292 ) @ SV240 ) ) )
= $true )
| ( ( preorder @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1113,plain,
! [SV293: $i,SV241: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SV241 ) @ SV293 ) )
= $false )
| ( ( ( SV241 != SV293 ) )
= $true )
| ( ( order @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1114,plain,
! [SV294: $i,SV242: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SV242 ) @ SV294 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV43 @ bool @ ( hAPP @ SV43 @ ( fun @ SV43 @ bool ) @ ( ord_less @ SV43 ) @ SV294 ) @ SV242 ) )
= $true )
| ( ( ( ti @ SV43 @ SV242 )
= ( ti @ SV43 @ SV294 ) )
= $true )
| ( ( linorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1115,plain,
! [SV295: $i,SV243: $i,SV44: $i] :
( ( ( ( ti @ SV44 @ SV243 )
= ( ti @ SV44 @ SV295 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SV243 ) @ SV295 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV44 @ bool @ ( hAPP @ SV44 @ ( fun @ SV44 @ bool ) @ ( ord_less @ SV44 ) @ SV295 ) @ SV243 ) )
= $true )
| ( ( linorder @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1116,plain,
! [SV245: $i,SV187: $i,SV296: $i,SV127: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SV296 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
= $false )
| ( ( ( ( hAPP @ SV47 @ SV127 @ SV296 @ SV187 )
!= ( ti @ SV127 @ SV245 ) )
| ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SV296 ) @ SV245 )
= ( ti @ SV47 @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1117,plain,
! [SV190: $i,SV297: $i,SV248: $i,SV130: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SV248 ) @ SV297 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SV190 ) @ SV297 ) )
| ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SV297 ) @ SV248 ) @ ( hAPP @ SV50 @ SV130 @ SV248 @ SV190 ) )
= ( ti @ SV50 @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1118,plain,
! [SV191: $i,SV249: $i,SV325: $i,SV298: $i,SV131: $i,SV51: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SV325 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SV325 ) )
| ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SV325 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1119,plain,
! [SV250: $i,SV192: $i,SV326: $i,SV299: $i,SV132: $i,SV52: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) ) )
= $true )
| ( ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
| ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1120,plain,
! [SV251: $i,SV193: $i,SV327: $i,SV300: $i,SV133: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) ) )
= $true )
| ( ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
!= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1121,plain,
! [SV252: $i,SV194: $i,SV301: $i,SV135: $i,SV55: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SV301 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
= $false )
| ( ( ( ( hAPP @ SV55 @ SV135 @ SV301 @ SV194 )
!= ( hAPP @ SV55 @ SV135 @ SV301 @ SV252 ) )
| ( ( ti @ SV55 @ SV194 )
= ( ti @ SV55 @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1122,plain,
! [SV195: $i,SV253: $i,SV136: $i,SV56: $i] :
( ( ( ( ( hAPP @ SV56 @ SV136 @ SV253 @ ( hAPP @ SV136 @ SV56 @ SV195 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
!= ( ti @ SV136 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) ) )
= $true )
| ( ( ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SV136 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SV253 )
= ( ti @ ( fun @ SV136 @ SV56 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SV136 ) @ SV253 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1123,plain,
! [SV196: $i,SV137: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SV137 ) ) @ SV196 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV137 ) @ SV57 ) ) @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV196 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1124,plain,
! [SV199: $i,SV328: $i,SV302: $i,SV255: $i,SV143: $i,SV64: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SV255 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SV302 ) @ SV328 ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SV255 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SV328 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1125,plain,
! [SV200: $i,SV329: $i,SV303: $i,SV256: $i,SV144: $i,SV66: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SV256 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SV303 ) @ SV329 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SV256 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SV329 @ SV200 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1126,plain,
! [SV201: $i,SV330: $i,SV304: $i,SV257: $i,SV145: $i,SV67: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SV257 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SV304 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SV330 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SV304 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SV257 @ SV201 ) ) @ SV330 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1127,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1128,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1129,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ~ ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1130,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1776 ) @ SY1777 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1777 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1776 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1131,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ! [SY2060: $i,SY2061: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2060 )
= ( ti @ arrow_1212486748le_alt @ SY2061 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2061 @ SY2060 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2060 ) @ SY2061 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1038]) ).
thf(1132,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ! [SY2062: $i,SY2063: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2062 )
= ( ti @ arrow_1212486748le_alt @ SY2063 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2063 @ SY2062 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2062 ) @ SY2063 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1133,plain,
! [SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ! [SY2064: $i] :
( ! [SY2065: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2064 ) @ SY2065 ) )
| ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SY2064 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1134,plain,
! [SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ! [SY2066: $i,SY2067: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SY2066 ) @ SY2067 ) )
| ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SY2067 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1135,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ~ ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1136,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ~ ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1137,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ~ ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1138,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ! [SY1802: $i,SY1803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1802 ) @ SY1803 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1803 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1802 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1139,plain,
! [SV347: $i,SV90: $i] :
( ( ( ! [SY2142: $i] :
( ( ( ti @ SV90 @ SV347 )
= ( ti @ SV90 @ SY2142 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV347 ) @ SY2142 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY2142 ) @ SV347 ) ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1140,plain,
! [SV90: $i] :
( ( ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) )
| ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1141,plain,
! [SV308: $i,SV91: $i,SV334: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV334 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SV334 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SV334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1142,plain,
! [SV309: $i,SV91: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV335 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV309 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV309 ) ) @ SV335 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV309 ) @ SV91 ) ) @ SV335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1143,plain,
! [SV348: $i,SV92: $i] :
( ( ( ( ( ti @ SV92 @ SV348 )
= ( top_top @ SV92 ) )
| ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SV348 ) @ ( top_top @ SV92 ) ) ) )
= $true )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1144,plain,
! [SV349: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SV349 ) @ ( top_top @ SV92 ) ) )
| ( ( ti @ SV92 @ SV349 )
!= ( top_top @ SV92 ) ) )
= $true )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1145,plain,
! [SV264: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SV264 ) ) @ arrow_1834574746e_Prof ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1146,plain,
! [SV264: $i] :
( ( ( ~ ~ ( ~ ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1147,plain,
! [SV265: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV350 ) @ arrow_1834574746e_Prof ) )
| ! [SY2143: $i,SY2144: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2143 ) @ SY2144 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV350 @ ( sK14_I @ SY2144 @ SY2143 @ SV350 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2143 ) @ SY2144 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SV350 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1148,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1149,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1150,plain,
! [SV351: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV351 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1151,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1152,plain,
! [SV352: $i,SV93: $i] :
( ( ( ! [SY2145: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV352 ) @ SY2145 ) )
| ( ( ti @ SV93 @ SY2145 )
!= ( ti @ SV93 @ SV352 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY2145 ) @ SV352 ) ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1153,plain,
! [SV353: $i,SV93: $i] :
( ( ( ! [SY2146: $i] :
( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV353 ) @ SY2146 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SY2146 ) @ SV353 ) )
| ( ( ti @ SV93 @ SY2146 )
= ( ti @ SV93 @ SV353 ) ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1154,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SV166 @ SV94 ) ) @ arrow_1834574746e_Prof ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1155,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1156,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i] :
( ( ! [SY2072: $i,SY2073: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SY2073 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2072 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2073 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2073 @ SY2072 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2072 ) @ SY2073 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1157,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i] :
( ( ! [SY2074: $i,SY2075: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SY2075 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2074 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2075 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2075 @ SY2074 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2074 ) @ SY2075 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1158,plain,
! [SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SV267 ) ) @ arrow_1834574746e_Prof ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1159,plain,
! [SV267: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1160,plain,
! [SV268: $i,SV354: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
| ! [SY2147: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2147 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SY2148: $i,SY2149: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2147 ) ) ) )
| ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2147 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1161,plain,
! [SV97: $i] :
( ( ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) )
| ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1162,plain,
! [SV355: $i,SV97: $i] :
( ( ( ! [SY2152: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV355 ) @ SY2152 ) )
| ( ( ti @ SV97 @ SV355 )
= ( ti @ SV97 @ SY2152 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY2152 ) @ SV355 ) ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1163,plain,
! [SV356: $i,SV214: $i,SV169: $i,SV98: $i] :
( ( ! [SY2153: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY2153 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SV169 @ SY2153 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SY2153 @ SV356 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1164,plain,
! [SV357: $i,SV214: $i,SV169: $i,SV98: $i] :
( ( ! [SY2154: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SY2154 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SV357 ) )
| ( ( hAPP @ SV98 @ SV169 @ SY2154 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SY2154 @ SV357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1165,plain,
! [SV99: $i,SV170: $i,SV215: $i,SV358: $i] :
( ( ! [SY2155: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SY2155 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2155 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SY2155 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY2155 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2155 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY2155 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SY2155 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SY2155 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2155 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SY2155 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SY2155 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2155 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1166,plain,
! [SV99: $i,SV170: $i,SV215: $i,SV359: $i] :
( ( ! [SY2156: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SY2156 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2156 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SY2156 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY2156 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2156 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY2156 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SY2156 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SY2156 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2156 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SY2156 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2156 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SY2156 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1167,plain,
! [SV336: $i,SV310: $i,SV100: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV310 ) @ SV336 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV100 @ bool @ SV336 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1168,plain,
! [SV311: $i,SV337: $i,SV100: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV100 @ bool @ SV337 @ SV311 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV311 ) @ SV337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1169,plain,
! [SV338: $i,SV312: $i,SV101: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( sK26_X1 @ SV338 @ SV312 @ SV101 ) ) ) )
= $true )
| ( ( ! [SY2127: $i,SY2128: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( hAPP @ SV312 @ ( product_prod @ SV101 @ SV312 ) @ ( hAPP @ SV101 @ ( fun @ SV312 @ ( product_prod @ SV101 @ SV312 ) ) @ ( product_Pair @ SV101 @ SV312 ) @ SY2127 ) @ SY2128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1170,plain,
! [SV339: $i,SV313: $i,SV101: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ ( hAPP @ SV313 @ ( product_prod @ SV101 @ SV313 ) @ ( hAPP @ SV101 @ ( fun @ SV313 @ ( product_prod @ SV101 @ SV313 ) ) @ ( product_Pair @ SV101 @ SV313 ) @ ( sK24_A_2 @ SV339 @ SV313 @ SV101 ) ) @ ( sK25_SY1332 @ SV339 @ SV313 @ SV101 ) ) ) ) )
= $true )
| ( ( ! [SY2129: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ SY2129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1171,plain,
! [SV271: $i,SV102: $i,SV216: $i,SV171: $i] :
( ( ! [SY2084: $i,SY2085: $i] :
( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SY2084 ) )
| ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SY2085 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2084 ) @ SY2085 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1172,plain,
! [SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ~ ( ~ ! [SY2086: $i] :
( ! [SY2087: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2086 ) @ SY2087 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY2086 ) ) )
| ~ ! [SY2088: $i,SY2089: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2088 ) @ SY2089 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2089 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1173,plain,
! [SV217: $i,SV272: $i,SV172: $i,SV103: $i] :
( ( ! [SY2090: $i,SY2091: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2090 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2091 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2091 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2090 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SY2090 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1174,plain,
! [SV217: $i,SV272: $i,SV172: $i,SV103: $i] :
( ( ! [SY2092: $i,SY2093: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SY2092 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2093 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SY2092 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SY2092 @ SV217 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1175,plain,
! [SV218: $i,SV173: $i,SV104: $i] :
( ( ( ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
= ( hAPP @ SV104 @ SV173 @ SV218 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1176,plain,
! [SV173: $i,SV218: $i,SV104: $i] :
( ( ( ( ( ti @ SV104 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
!= ( ti @ SV104 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1177,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1178,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1179,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1180,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1181,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) ) )
| ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1182,plain,
! [SV341: $i,SV361: $i,SV174: $i,SV105: $i] :
( ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
| ~ ( ~ ! [SY2157: $i,SY2158: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV341 ) ) )
| ~ ! [SY2159: $i,SY2160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV361 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1183,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1184,plain,
! [SV363: $i,SV343: $i,SV175: $i,SV106: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
| ! [SY2161: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2161 ) @ SV363 ) )
| ! [SY2162: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2162 ) @ SV363 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SY2161 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SY2162 ) )
| ( ( ti @ SV106 @ SY2161 )
= ( ti @ SV106 @ SY2162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1185,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1186,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
| ~ ~ ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1187,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1188,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1189,plain,
! [SV109: $i,SV178: $i,SV273: $i,SV220: $i,SV346: $i,SV314: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1190,plain,
! [SV274: $i,SV315: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SV315 @ SV274 ) ) @ arrow_1834574746e_Prof ) )
| ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV274 @ ( sK1_X_1 @ SV315 @ SV274 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SV315 @ SV274 ) @ SV315 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1191,plain,
! [SV316: $i,SV275: $i] :
( ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV275 ) @ SV316 ) )
= $false )
| ( ( ! [SY2126: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2126 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV275 @ SY2126 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2126 @ SV316 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1192,plain,
! [SV227: $i,SV279: $i,SV28: $i] :
( ( ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV279 ) @ SV227 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV28 @ bool @ ( hAPP @ SV28 @ ( fun @ SV28 @ bool ) @ ( ord_less @ SV28 ) @ SV227 ) @ SV279 ) )
= $false )
| ( ( preorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1193,plain,
! [SV228: $i,SV318: $i,SV280: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV280 ) @ SV318 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV280 ) )
| ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV318 ) ) )
= $true )
| ( ( order @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1194,plain,
! [SV229: $i,SV319: $i,SV281: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV319 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV319 ) @ SV229 ) )
| ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV229 ) ) )
= $true )
| ( ( preorder @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1195,plain,
! [SV230: $i,SV320: $i,SV282: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV282 ) @ SV320 ) )
= $false )
| ( ( ( SV282 != SV230 )
| ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV230 ) @ SV320 ) ) )
= $true )
| ( ( order @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1196,plain,
! [SV231: $i,SV321: $i,SV283: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV321 ) )
= $false )
| ( ( ( SV321 != SV231 )
| ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV231 ) ) )
= $true )
| ( ( ord @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1197,plain,
! [SV232: $i,SV33: $i,SV322: $i,SV284: $i] :
( ( ( SV284 = SV322 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV322 ) )
| ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV284 ) ) )
= $true )
| ( ( order @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1198,plain,
! [SV233: $i,SV34: $i,SV323: $i,SV285: $i] :
( ( ( SV285 = SV323 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV323 ) @ SV233 ) )
| ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV285 ) @ SV233 ) ) )
= $true )
| ( ( ord @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1199,plain,
! [SV234: $i,SV286: $i,SV35: $i] :
( ( ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV286 ) @ SV234 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV35 @ bool @ ( hAPP @ SV35 @ ( fun @ SV35 @ bool ) @ ( ord_less @ SV35 ) @ SV234 ) @ SV286 ) )
= $false )
| ( ( order @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1200,plain,
! [SV235: $i,SV287: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV287 ) @ SV235 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV36 @ bool @ ( hAPP @ SV36 @ ( fun @ SV36 @ bool ) @ ( ord_less @ SV36 ) @ SV235 ) @ SV287 ) )
= $false )
| ( ( preorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1201,plain,
! [SV236: $i,SV324: $i,SV288: $i,SV37: $i] :
( ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV288 ) @ SV324 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV324 ) @ SV288 ) )
| ( hBOOL @ SV236 ) )
= $true )
| ( ( preorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1202,plain,
! [SV38: $i,SV237: $i,SV289: $i] :
( ( ( SV289 = SV237 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV38 @ bool @ ( hAPP @ SV38 @ ( fun @ SV38 @ bool ) @ ( ord_less @ SV38 ) @ SV237 ) @ SV289 ) )
= $false )
| ( ( order @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1203,plain,
! [SV39: $i,SV290: $i,SV238: $i] :
( ( ( SV238 = SV290 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV39 @ bool @ ( hAPP @ SV39 @ ( fun @ SV39 @ bool ) @ ( ord_less @ SV39 ) @ SV238 ) @ SV290 ) )
= $false )
| ( ( order @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1204,plain,
! [SV239: $i,SV291: $i,SV40: $i] :
( ( ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV291 ) @ SV239 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV40 @ bool @ ( hAPP @ SV40 @ ( fun @ SV40 @ bool ) @ ( ord_less @ SV40 ) @ SV239 ) @ SV291 ) )
= $false )
| ( ( preorder @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1205,plain,
! [SV240: $i,SV292: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV292 ) @ SV240 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV41 @ bool @ ( hAPP @ SV41 @ ( fun @ SV41 @ bool ) @ ( ord_less @ SV41 ) @ SV240 ) @ SV292 ) )
= $false )
| ( ( preorder @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1206,plain,
! [SV42: $i,SV293: $i,SV241: $i] :
( ( ( SV241 = SV293 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV42 @ bool @ ( hAPP @ SV42 @ ( fun @ SV42 @ bool ) @ ( ord_less @ SV42 ) @ SV241 ) @ SV293 ) )
= $false )
| ( ( order @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1207,plain,
! [SV245: $i,SV187: $i,SV296: $i,SV127: $i,SV47: $i] :
( ( ( ( ( hAPP @ SV47 @ SV127 @ SV296 @ SV187 )
!= ( ti @ SV127 @ SV245 ) ) )
= $true )
| ( ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SV296 ) @ SV245 )
= ( ti @ SV47 @ SV187 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SV296 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1208,plain,
! [SV248: $i,SV130: $i,SV297: $i,SV190: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SV190 ) @ SV297 ) ) )
= $true )
| ( ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SV297 ) @ SV248 ) @ ( hAPP @ SV50 @ SV130 @ SV248 @ SV190 ) )
= ( ti @ SV50 @ SV190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SV248 ) @ SV297 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1209,plain,
! [SV191: $i,SV249: $i,SV325: $i,SV298: $i,SV131: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SV325 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SV325 ) )
| ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SV325 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1210,plain,
! [SV250: $i,SV192: $i,SV326: $i,SV299: $i,SV132: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
= $false )
| ( ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
| ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1211,plain,
! [SV251: $i,SV193: $i,SV327: $i,SV300: $i,SV133: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
= $false )
| ( ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
!= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1212,plain,
! [SV252: $i,SV194: $i,SV301: $i,SV135: $i,SV55: $i] :
( ( ( ( ( hAPP @ SV55 @ SV135 @ SV301 @ SV194 )
!= ( hAPP @ SV55 @ SV135 @ SV301 @ SV252 ) ) )
= $true )
| ( ( ( ti @ SV55 @ SV194 )
= ( ti @ SV55 @ SV252 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SV301 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1213,plain,
! [SV195: $i,SV253: $i,SV136: $i,SV56: $i] :
( ( ( ( hAPP @ SV56 @ SV136 @ SV253 @ ( hAPP @ SV136 @ SV56 @ SV195 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
= ( ti @ SV136 @ ( sK9_X_1 @ SV253 @ SV195 @ SV136 @ SV56 ) ) )
= $false )
| ( ( ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) @ ( hAPP @ ( fun @ SV56 @ bool ) @ ( fun @ ( fun @ SV56 @ SV136 ) @ ( fun @ SV136 @ SV56 ) ) @ ( hilbert_inv_into @ SV56 @ SV136 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) @ SV253 )
= ( ti @ ( fun @ SV136 @ SV56 ) @ SV195 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV56 @ bool ) @ bool @ ( hAPP @ ( fun @ SV56 @ SV136 ) @ ( fun @ ( fun @ SV56 @ bool ) @ bool ) @ ( inj_on @ SV56 @ SV136 ) @ SV253 ) @ ( top_top @ ( fun @ SV56 @ bool ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1214,plain,
! [SV196: $i,SV57: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV137 ) @ SV57 ) ) @ SV196 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV57 ) @ SV137 ) ) @ SV196 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV196 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1215,plain,
! [SV199: $i,SV328: $i,SV302: $i,SV255: $i,SV143: $i,SV64: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SV255 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SV302 ) @ SV328 ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SV255 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SV328 @ SV199 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1216,plain,
! [SV200: $i,SV329: $i,SV303: $i,SV256: $i,SV144: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SV256 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SV303 ) @ SV329 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SV303 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SV256 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SV329 @ SV200 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1217,plain,
! [SV201: $i,SV330: $i,SV304: $i,SV257: $i,SV145: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SV257 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SV304 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SV330 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SV304 ) )
| ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SV257 @ SV201 ) ) @ SV330 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1218,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1219,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1220,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1221,plain,
! [SV162: $i,SV86: $i] :
( ( ! [SY1776: $i,SY1777: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1776 ) @ SY1777 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1777 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1776 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1222,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i,SV366: $i] :
( ( ! [SY2163: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SY2163 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SY2163 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2163 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2163 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SY2163 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SY2163 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SY2163 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SY2163 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1223,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i,SV367: $i] :
( ( ! [SY2164: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SY2164 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SY2164 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2164 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2164 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SY2164 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SY2164 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SY2164 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SY2164 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1224,plain,
! [SV368: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ! [SY2165: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV368 ) @ SY2165 ) )
| ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1225,plain,
! [SV369: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ! [SY2166: $i] :
( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV369 ) @ SY2166 ) )
| ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SY2166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1226,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1227,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1136]) ).
thf(1228,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1229,plain,
! [SV165: $i,SV89: $i] :
( ( ! [SY1802: $i,SY1803: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1802 ) @ SY1803 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1803 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1802 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1230,plain,
! [SV370: $i,SV347: $i,SV90: $i] :
( ( ( ( ( ti @ SV90 @ SV347 )
= ( ti @ SV90 @ SV370 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV347 ) @ SV370 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV370 ) @ SV347 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1231,plain,
! [SV90: $i] :
( ( ( ~ ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1232,plain,
! [SV90: $i] :
( ( ( ~ ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1140]) ).
thf(1233,plain,
! [SV308: $i,SV91: $i,SV334: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV334 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SV334 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SV334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1234,plain,
! [SV309: $i,SV91: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV335 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV309 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV309 ) ) @ SV335 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV309 ) @ SV91 ) ) @ SV335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1235,plain,
! [SV348: $i,SV92: $i] :
( ( ( ( ti @ SV92 @ SV348 )
= ( top_top @ SV92 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SV348 ) @ ( top_top @ SV92 ) ) )
= $true )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1236,plain,
! [SV349: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SV349 ) @ ( top_top @ SV92 ) ) ) )
= $true )
| ( ( ( ( ti @ SV92 @ SV349 )
!= ( top_top @ SV92 ) ) )
= $true )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1237,plain,
! [SV264: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK15_X_1 @ SV264 ) ) @ arrow_1834574746e_Prof ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1238,plain,
! [SV264: $i] :
( ( ( ~ ( ~ ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1239,plain,
! [SV265: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV350 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ! [SY2143: $i,SY2144: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2143 ) @ SY2144 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV350 @ ( sK14_I @ SY2144 @ SY2143 @ SV350 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2143 ) @ SY2144 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SV350 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1240,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1241,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1242,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1243,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1244,plain,
! [SV351: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV351 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1245,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1246,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1151]) ).
thf(1247,plain,
! [SV371: $i,SV352: $i,SV93: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV352 ) @ SV371 ) )
| ( ( ti @ SV93 @ SV371 )
!= ( ti @ SV93 @ SV352 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV371 ) @ SV352 ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1248,plain,
! [SV372: $i,SV353: $i,SV93: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV353 ) @ SV372 ) )
| ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV372 ) @ SV353 ) )
| ( ( ti @ SV93 @ SV372 )
= ( ti @ SV93 @ SV353 ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1249,plain,
! [SV94: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK3_X_1 @ SV166 @ SV94 ) ) @ arrow_1834574746e_Prof ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1250,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1251,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i,SV373: $i] :
( ( ! [SY2167: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SY2167 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2167 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SY2167 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2167 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2167 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SY2167 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SY2167 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SY2167 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SY2167 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1252,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i,SV374: $i] :
( ( ! [SY2168: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SY2168 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SY2168 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SY2168 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2168 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2168 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SY2168 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SY2168 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SY2168 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SY2168 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1253,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK20_X_1 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1254,plain,
! [SV267: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1255,plain,
! [SV268: $i,SV354: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ! [SY2147: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2147 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SY2148: $i,SY2149: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2147 ) ) ) )
| ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2147 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1256,plain,
! [SV97: $i] :
( ( ( ~ ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1257,plain,
! [SV97: $i] :
( ( ( ~ ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1258,plain,
! [SV375: $i,SV355: $i,SV97: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV355 ) @ SV375 ) )
| ( ( ti @ SV97 @ SV355 )
= ( ti @ SV97 @ SV375 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV375 ) @ SV355 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1259,plain,
! [SV356: $i,SV214: $i,SV376: $i,SV169: $i,SV98: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV376 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( hAPP @ SV98 @ SV169 @ SV376 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SV376 @ SV356 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1260,plain,
! [SV357: $i,SV214: $i,SV377: $i,SV169: $i,SV98: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV377 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
| ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SV357 ) )
| ( ( hAPP @ SV98 @ SV169 @ SV377 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SV377 @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1261,plain,
! [SV99: $i,SV170: $i,SV215: $i,SV378: $i,SV358: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1262,plain,
! [SV99: $i,SV170: $i,SV215: $i,SV379: $i,SV359: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1263,plain,
! [SV336: $i,SV310: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV310 ) @ SV336 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV100 @ bool @ SV336 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1264,plain,
! [SV311: $i,SV337: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP @ SV100 @ bool @ SV337 @ SV311 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV100 @ bool ) @ bool @ ( hAPP @ SV100 @ ( fun @ ( fun @ SV100 @ bool ) @ bool ) @ ( member @ SV100 ) @ SV311 ) @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1265,plain,
! [SV338: $i,SV312: $i,SV101: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( sK26_X1 @ SV338 @ SV312 @ SV101 ) ) )
= $false )
| ( ( ! [SY2127: $i,SY2128: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( hAPP @ SV312 @ ( product_prod @ SV101 @ SV312 ) @ ( hAPP @ SV101 @ ( fun @ SV312 @ ( product_prod @ SV101 @ SV312 ) ) @ ( product_Pair @ SV101 @ SV312 ) @ SY2127 ) @ SY2128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1266,plain,
! [SV339: $i,SV313: $i,SV101: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ ( hAPP @ SV313 @ ( product_prod @ SV101 @ SV313 ) @ ( hAPP @ SV101 @ ( fun @ SV313 @ ( product_prod @ SV101 @ SV313 ) ) @ ( product_Pair @ SV101 @ SV313 ) @ ( sK24_A_2 @ SV339 @ SV313 @ SV101 ) ) @ ( sK25_SY1332 @ SV339 @ SV313 @ SV101 ) ) ) )
= $false )
| ( ( ! [SY2129: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ SY2129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1267,plain,
! [SV271: $i,SV102: $i,SV380: $i,SV216: $i,SV171: $i] :
( ( ! [SY2169: $i] :
( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SV380 ) )
| ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SY2169 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV380 ) @ SY2169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1268,plain,
! [SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ~ ! [SY2086: $i] :
( ! [SY2087: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2086 ) @ SY2087 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY2086 ) ) )
| ~ ! [SY2088: $i,SY2089: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2088 ) @ SY2089 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2089 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1269,plain,
! [SV217: $i,SV272: $i,SV381: $i,SV172: $i,SV103: $i] :
( ( ! [SY2170: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SY2170 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2170 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2170 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1270,plain,
! [SV217: $i,SV272: $i,SV382: $i,SV172: $i,SV103: $i] :
( ( ! [SY2171: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SY2171 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SY2171 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SY2171 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1271,plain,
! [SV173: $i,SV218: $i,SV104: $i] :
( ( ( ( ti @ SV104 @ ( sK7_X_1 @ SV218 @ SV173 @ SV104 ) )
= ( ti @ SV104 @ ( sK8_SY1309 @ SV218 @ SV173 @ SV104 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV104 @ bool ) @ bool @ ( hAPP @ ( fun @ SV104 @ SV173 ) @ ( fun @ ( fun @ SV104 @ bool ) @ bool ) @ ( inj_on @ SV104 @ SV173 ) @ SV218 ) @ ( top_top @ ( fun @ SV104 @ bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1272,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1273,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1274,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1275,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1276,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1277,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1278,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1279,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1280,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1281,plain,
! [SV341: $i,SV361: $i,SV174: $i,SV105: $i] :
( ( ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
!= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2157: $i,SY2158: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV341 ) ) )
| ~ ! [SY2159: $i,SY2160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV361 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1282,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1283,plain,
! [SV363: $i,SV343: $i,SV175: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) ) )
= $true )
| ( ( ! [SY2161: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2161 ) @ SV363 ) )
| ! [SY2162: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2162 ) @ SV363 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SY2161 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SY2162 ) )
| ( ( ti @ SV106 @ SY2161 )
= ( ti @ SV106 @ SY2162 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1284,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1185]) ).
thf(1285,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1185]) ).
thf(1286,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1287,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1288,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1289,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1290,plain,
! [SV109: $i,SV178: $i,SV346: $i,SV314: $i,SV273: $i,SV220: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1291,plain,
! [SV274: $i,SV315: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SV315 @ SV274 ) ) @ arrow_1834574746e_Prof ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1292,plain,
! [SV315: $i,SV274: $i] :
( ( ( ~ ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV274 @ ( sK1_X_1 @ SV315 @ SV274 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SV315 @ SV274 ) @ SV315 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1293,plain,
! [SV316: $i,SV275: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV383 ) @ arrow_1834574746e_Prof ) )
| ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV275 @ SV383 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV383 @ SV316 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV275 ) @ SV316 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1294,plain,
! [SV318: $i,SV280: $i,SV228: $i,SV29: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV280 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV318 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV280 ) @ SV318 ) )
= $false )
| ( ( order @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1295,plain,
! [SV281: $i,SV229: $i,SV319: $i,SV30: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV319 ) @ SV229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV229 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV319 ) )
= $false )
| ( ( preorder @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1296,plain,
! [SV320: $i,SV31: $i,SV230: $i,SV282: $i] :
( ( ( ( SV282 != SV230 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV230 ) @ SV320 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV282 ) @ SV320 ) )
= $false )
| ( ( order @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1297,plain,
! [SV283: $i,SV32: $i,SV231: $i,SV321: $i] :
( ( ( ( SV321 != SV231 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV231 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV321 ) )
= $false )
| ( ( ord @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1298,plain,
! [SV284: $i,SV322: $i,SV232: $i,SV33: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV322 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV284 ) )
= $true )
| ( ( SV284 = SV322 )
= $false )
| ( ( order @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1299,plain,
! [SV285: $i,SV233: $i,SV323: $i,SV34: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV323 ) @ SV233 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV285 ) @ SV233 ) )
= $true )
| ( ( SV285 = SV323 )
= $false )
| ( ( ord @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1300,plain,
! [SV236: $i,SV288: $i,SV324: $i,SV37: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV324 ) @ SV288 ) ) )
= $true )
| ( ( hBOOL @ SV236 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV288 ) @ SV324 ) )
= $false )
| ( ( preorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1301,plain,
! [SV245: $i,SV187: $i,SV296: $i,SV127: $i,SV47: $i] :
( ( ( ( hAPP @ SV47 @ SV127 @ SV296 @ SV187 )
= ( ti @ SV127 @ SV245 ) )
= $false )
| ( ( ( hAPP @ SV127 @ SV47 @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) @ ( hAPP @ ( fun @ SV47 @ bool ) @ ( fun @ ( fun @ SV47 @ SV127 ) @ ( fun @ SV127 @ SV47 ) ) @ ( hilbert_inv_into @ SV47 @ SV127 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) @ SV296 ) @ SV245 )
= ( ti @ SV47 @ SV187 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV47 @ bool ) @ bool @ ( hAPP @ ( fun @ SV47 @ SV127 ) @ ( fun @ ( fun @ SV47 @ bool ) @ bool ) @ ( inj_on @ SV47 @ SV127 ) @ SV296 ) @ ( top_top @ ( fun @ SV47 @ bool ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1302,plain,
! [SV248: $i,SV130: $i,SV297: $i,SV190: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ SV50 @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( member @ SV50 ) @ SV190 ) @ SV297 ) )
= $false )
| ( ( ( hAPP @ SV130 @ SV50 @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) @ ( hAPP @ ( fun @ SV50 @ bool ) @ ( fun @ ( fun @ SV50 @ SV130 ) @ ( fun @ SV130 @ SV50 ) ) @ ( hilbert_inv_into @ SV50 @ SV130 ) @ SV297 ) @ SV248 ) @ ( hAPP @ SV50 @ SV130 @ SV248 @ SV190 ) )
= ( ti @ SV50 @ SV190 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV50 @ bool ) @ bool @ ( hAPP @ ( fun @ SV50 @ SV130 ) @ ( fun @ ( fun @ SV50 @ bool ) @ bool ) @ ( inj_on @ SV50 @ SV130 ) @ SV248 ) @ SV297 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1303,plain,
! [SV191: $i,SV298: $i,SV131: $i,SV325: $i,SV249: $i,SV51: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SV325 ) ) )
= $true )
| ( ( ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SV325 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1304,plain,
! [SV299: $i,SV132: $i,SV326: $i,SV250: $i,SV192: $i,SV52: $i] :
( ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
| ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1305,plain,
! [SV327: $i,SV251: $i,SV193: $i,SV300: $i,SV133: $i,SV53: $i] :
( ( ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
!= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1306,plain,
! [SV252: $i,SV194: $i,SV301: $i,SV135: $i,SV55: $i] :
( ( ( ( hAPP @ SV55 @ SV135 @ SV301 @ SV194 )
= ( hAPP @ SV55 @ SV135 @ SV301 @ SV252 ) )
= $false )
| ( ( ( ti @ SV55 @ SV194 )
= ( ti @ SV55 @ SV252 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV55 @ bool ) @ bool @ ( hAPP @ ( fun @ SV55 @ SV135 ) @ ( fun @ ( fun @ SV55 @ bool ) @ bool ) @ ( inj_on @ SV55 @ SV135 ) @ SV301 ) @ ( top_top @ ( fun @ SV55 @ bool ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1307,plain,
! [SV302: $i,SV328: $i,SV199: $i,SV255: $i,SV64: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SV255 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SV328 @ SV199 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SV302 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SV255 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SV302 ) @ SV328 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1308,plain,
! [SV329: $i,SV256: $i,SV144: $i,SV303: $i,SV200: $i,SV66: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SV303 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SV256 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SV329 @ SV200 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SV256 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SV303 ) @ SV329 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1309,plain,
! [SV330: $i,SV257: $i,SV145: $i,SV304: $i,SV201: $i,SV67: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SV304 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SV257 @ SV201 ) ) @ SV330 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SV257 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SV304 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SV330 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1310,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) )
| ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1311,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) )
| ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1312,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) )
| ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1313,plain,
! [SV384: $i,SV162: $i,SV86: $i] :
( ( ! [SY2172: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV384 ) @ SY2172 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY2172 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1314,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i,SV385: $i,SV366: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1315,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i,SV386: $i,SV367: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1316,plain,
! [SV368: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ( ! [SY2165: $i] :
( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV368 ) @ SY2165 ) ) )
= $true )
| ( ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1317,plain,
! [SV387: $i,SV369: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV369 ) @ SV387 ) )
| ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1318,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) )
| ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1319,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) )
| ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1320,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) )
| ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1321,plain,
! [SV388: $i,SV165: $i,SV89: $i] :
( ( ! [SY2173: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV388 ) @ SY2173 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY2173 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1322,plain,
! [SV370: $i,SV347: $i,SV90: $i] :
( ( ( ( ti @ SV90 @ SV347 )
= ( ti @ SV90 @ SV370 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV347 ) @ SV370 ) )
| ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV370 ) @ SV347 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1323,plain,
! [SV90: $i] :
( ( ( ! [SY1553: $i,SY1554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1553 ) @ SY1554 ) )
| ( ( ti @ SV90 @ SY1553 )
!= ( ti @ SV90 @ SY1554 ) ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1324,plain,
! [SV90: $i] :
( ( ( ! [SY1555: $i,SY1556: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY1556 ) @ SY1555 ) )
| ( ( ti @ SV90 @ SY1555 )
!= ( ti @ SV90 @ SY1556 ) ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1232]) ).
thf(1325,plain,
! [SV334: $i,SV308: $i,SV91: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SV334 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SV334 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV334 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1326,plain,
! [SV335: $i,SV309: $i,SV91: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV309 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV309 ) ) @ SV335 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV309 ) @ SV91 ) ) @ SV335 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV335 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1327,plain,
! [SV349: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SV349 ) @ ( top_top @ SV92 ) ) )
= $false )
| ( ( ( ( ti @ SV92 @ SV349 )
!= ( top_top @ SV92 ) ) )
= $true )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1328,plain,
! [SV264: $i] :
( ( ( ~ ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1329,plain,
! [SV265: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV350 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ! [SY2143: $i,SY2144: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2143 ) @ SY2144 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV350 @ ( sK14_I @ SY2144 @ SY2143 @ SV350 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2143 ) @ SY2144 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SV350 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1330,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1331,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1332,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1333,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1334,plain,
! [SV351: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV351 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1335,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1336,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1337,plain,
! [SV371: $i,SV352: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV352 ) @ SV371 ) )
= $true )
| ( ( ( ( ti @ SV93 @ SV371 )
!= ( ti @ SV93 @ SV352 ) )
| ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV371 ) @ SV352 ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1338,plain,
! [SV372: $i,SV353: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV353 ) @ SV372 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV372 ) @ SV353 ) )
| ( ( ti @ SV93 @ SV372 )
= ( ti @ SV93 @ SV353 ) ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1339,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1340,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i,SV389: $i,SV373: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1341,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i,SV390: $i,SV374: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1342,plain,
! [SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
| ~ ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1343,plain,
! [SV268: $i,SV354: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ! [SY2147: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SY2147 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SY2148: $i,SY2149: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK19_I @ SY2149 @ SY2148 @ SY2147 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2148 ) @ SY2149 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2147 ) ) ) )
| ~ ! [SY2150: $i,SY2151: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SY2147 @ ( sK18_I @ SY2151 @ SY2150 @ SY2147 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SY2147 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2150 ) @ SY2151 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1344,plain,
! [SV97: $i] :
( ( ( ! [SY1576: $i,SY1577: $i] :
( ( ( ti @ SV97 @ SY1576 )
!= ( ti @ SV97 @ SY1577 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1576 ) @ SY1577 ) ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1345,plain,
! [SV97: $i] :
( ( ( ! [SY1578: $i,SY1579: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1579 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY1578 ) @ SY1579 ) ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1346,plain,
! [SV375: $i,SV355: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV355 ) @ SV375 ) )
= $true )
| ( ( ( ( ti @ SV97 @ SV355 )
= ( ti @ SV97 @ SV375 ) )
| ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV375 ) @ SV355 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1347,plain,
! [SV356: $i,SV214: $i,SV376: $i,SV169: $i,SV98: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV376 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) ) )
= $true )
| ( ( ( ( hAPP @ SV98 @ SV169 @ SV376 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SV376 @ SV356 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SV356 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1348,plain,
! [SV357: $i,SV214: $i,SV377: $i,SV169: $i,SV98: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV377 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) ) )
= $true )
| ( ( ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SV357 ) )
| ( ( hAPP @ SV98 @ SV169 @ SV377 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SV377 @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1349,plain,
! [SV99: $i,SV170: $i,SV215: $i,SV378: $i,SV358: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1350,plain,
! [SV99: $i,SV170: $i,SV215: $i,SV379: $i,SV359: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1351,plain,
! [SV391: $i,SV338: $i,SV312: $i,SV101: $i] :
( ( ( ! [SY2174: $i] : ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( hAPP @ SV312 @ ( product_prod @ SV101 @ SV312 ) @ ( hAPP @ SV101 @ ( fun @ SV312 @ ( product_prod @ SV101 @ SV312 ) ) @ ( product_Pair @ SV101 @ SV312 ) @ SV391 ) @ SY2174 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( sK26_X1 @ SV338 @ SV312 @ SV101 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1352,plain,
! [SV392: $i,SV339: $i,SV313: $i,SV101: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ SV392 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV313 ) @ bool @ SV339 @ ( hAPP @ SV313 @ ( product_prod @ SV101 @ SV313 ) @ ( hAPP @ SV101 @ ( fun @ SV313 @ ( product_prod @ SV101 @ SV313 ) ) @ ( product_Pair @ SV101 @ SV313 ) @ ( sK24_A_2 @ SV339 @ SV313 @ SV101 ) ) @ ( sK25_SY1332 @ SV339 @ SV313 @ SV101 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1353,plain,
! [SV393: $i,SV271: $i,SV102: $i,SV380: $i,SV216: $i,SV171: $i] :
( ( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SV380 ) )
| ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SV393 ) )
| ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV380 ) @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1354,plain,
! [SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ~ ! [SY2086: $i] :
( ! [SY2087: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2086 ) @ SY2087 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY2086 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1268]) ).
thf(1355,plain,
! [SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ~ ! [SY2088: $i,SY2089: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2088 ) @ SY2089 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2089 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1268]) ).
thf(1356,plain,
! [SV217: $i,SV272: $i,SV394: $i,SV381: $i,SV172: $i,SV103: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1357,plain,
! [SV217: $i,SV272: $i,SV395: $i,SV382: $i,SV172: $i,SV103: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1358,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1359,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1360,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1361,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1275]) ).
thf(1362,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1363,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1364,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1278]) ).
thf(1365,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1366,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1367,plain,
! [SV341: $i,SV361: $i,SV174: $i,SV105: $i] :
( ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false )
| ( ( ~ ( ~ ! [SY2157: $i,SY2158: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV341 ) ) )
| ~ ! [SY2159: $i,SY2160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV361 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1368,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1369,plain,
! [SV363: $i,SV343: $i,SV175: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false )
| ( ( ! [SY2161: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2161 ) @ SV363 ) )
| ! [SY2162: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2162 ) @ SV363 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SY2161 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SY2162 ) )
| ( ( ti @ SV106 @ SY2161 )
= ( ti @ SV106 @ SY2162 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1370,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1284]) ).
thf(1371,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1372,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1373,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1374,plain,
! [SV364: $i,SV344: $i,SV108: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1375,plain,
! [SV365: $i,SV345: $i,SV108: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1376,plain,
! [SV109: $i,SV178: $i,SV220: $i,SV346: $i,SV273: $i,SV314: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1377,plain,
! [SV274: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK1_X_1 @ SV315 @ SV274 ) ) @ arrow_1834574746e_Prof ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1291]) ).
thf(1378,plain,
! [SV315: $i,SV274: $i] :
( ( ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV274 @ ( sK1_X_1 @ SV315 @ SV274 ) )
!= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SV315 @ SV274 ) @ SV315 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1379,plain,
! [SV316: $i,SV275: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV383 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV275 @ SV383 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV383 @ SV316 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV275 ) @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1380,plain,
! [SV318: $i,SV280: $i,SV228: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV280 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV228 ) @ SV318 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV29 @ bool @ ( hAPP @ SV29 @ ( fun @ SV29 @ bool ) @ ( ord_less @ SV29 ) @ SV280 ) @ SV318 ) )
= $false )
| ( ( order @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1381,plain,
! [SV281: $i,SV229: $i,SV319: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV319 ) @ SV229 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV229 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV30 @ bool @ ( hAPP @ SV30 @ ( fun @ SV30 @ bool ) @ ( ord_less @ SV30 ) @ SV281 ) @ SV319 ) )
= $false )
| ( ( preorder @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1382,plain,
! [SV320: $i,SV31: $i,SV230: $i,SV282: $i] :
( ( ( SV282 = SV230 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV230 ) @ SV320 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV31 @ bool @ ( hAPP @ SV31 @ ( fun @ SV31 @ bool ) @ ( ord_less @ SV31 ) @ SV282 ) @ SV320 ) )
= $false )
| ( ( order @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1383,plain,
! [SV283: $i,SV32: $i,SV231: $i,SV321: $i] :
( ( ( SV321 = SV231 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV231 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV32 @ bool @ ( hAPP @ SV32 @ ( fun @ SV32 @ bool ) @ ( ord_less @ SV32 ) @ SV283 ) @ SV321 ) )
= $false )
| ( ( ord @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1384,plain,
! [SV284: $i,SV322: $i,SV232: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV322 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV33 @ bool @ ( hAPP @ SV33 @ ( fun @ SV33 @ bool ) @ ( ord_less @ SV33 ) @ SV232 ) @ SV284 ) )
= $true )
| ( ( SV284 = SV322 )
= $false )
| ( ( order @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1385,plain,
! [SV285: $i,SV233: $i,SV323: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV323 ) @ SV233 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV34 @ bool @ ( hAPP @ SV34 @ ( fun @ SV34 @ bool ) @ ( ord_less @ SV34 ) @ SV285 ) @ SV233 ) )
= $true )
| ( ( SV285 = SV323 )
= $false )
| ( ( ord @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1386,plain,
! [SV236: $i,SV288: $i,SV324: $i,SV37: $i] :
( ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV324 ) @ SV288 ) )
= $false )
| ( ( hBOOL @ SV236 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV37 @ bool @ ( hAPP @ SV37 @ ( fun @ SV37 @ bool ) @ ( ord_less @ SV37 ) @ SV288 ) @ SV324 ) )
= $false )
| ( ( preorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1387,plain,
! [SV191: $i,SV298: $i,SV131: $i,SV325: $i,SV249: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SV325 ) )
= $false )
| ( ( ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
!= ( ti @ SV131 @ SV191 ) )
| ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SV325 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1388,plain,
! [SV299: $i,SV132: $i,SV250: $i,SV326: $i,SV192: $i,SV52: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
| ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true )
| ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1389,plain,
! [SV327: $i,SV251: $i,SV193: $i,SV300: $i,SV133: $i,SV53: $i] :
( ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1390,plain,
! [SV328: $i,SV255: $i,SV143: $i,SV302: $i,SV199: $i,SV64: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV64 @ bool ) @ bool @ ( hAPP @ SV64 @ ( fun @ ( fun @ SV64 @ bool ) @ bool ) @ ( member @ SV64 ) @ SV199 ) @ SV302 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV143 @ bool ) @ bool @ ( hAPP @ SV143 @ ( fun @ ( fun @ SV143 @ bool ) @ bool ) @ ( member @ SV143 ) @ ( hAPP @ SV64 @ SV143 @ SV255 @ SV199 ) ) @ ( hAPP @ SV64 @ ( fun @ SV143 @ bool ) @ SV328 @ SV199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV64 @ SV143 ) @ ( fun @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV64 @ SV143 ) ) @ SV255 ) @ ( hAPP @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) @ ( hAPP @ ( fun @ SV64 @ bool ) @ ( fun @ ( fun @ SV64 @ ( fun @ SV143 @ bool ) ) @ ( fun @ ( fun @ SV64 @ SV143 ) @ bool ) ) @ ( pi @ SV64 @ SV143 ) @ SV302 ) @ SV328 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1391,plain,
! [SV329: $i,SV256: $i,SV144: $i,SV303: $i,SV200: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV66 @ bool ) @ bool @ ( hAPP @ SV66 @ ( fun @ ( fun @ SV66 @ bool ) @ bool ) @ ( member @ SV66 ) @ SV200 ) @ SV303 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV144 @ bool ) @ bool @ ( hAPP @ SV144 @ ( fun @ ( fun @ SV144 @ bool ) @ bool ) @ ( member @ SV144 ) @ ( hAPP @ SV66 @ SV144 @ SV256 @ SV200 ) ) @ ( hAPP @ SV66 @ ( fun @ SV144 @ bool ) @ SV329 @ SV200 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV66 @ SV144 ) @ ( fun @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV66 @ SV144 ) ) @ SV256 ) @ ( hAPP @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) @ ( hAPP @ ( fun @ SV66 @ bool ) @ ( fun @ ( fun @ SV66 @ ( fun @ SV144 @ bool ) ) @ ( fun @ ( fun @ SV66 @ SV144 ) @ bool ) ) @ ( pi @ SV66 @ SV144 ) @ SV303 ) @ SV329 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1392,plain,
! [SV330: $i,SV257: $i,SV145: $i,SV304: $i,SV201: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV67 @ bool ) @ bool @ ( hAPP @ SV67 @ ( fun @ ( fun @ SV67 @ bool ) @ bool ) @ ( member @ SV67 ) @ SV201 ) @ SV304 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV145 @ bool ) @ bool @ ( hAPP @ SV145 @ ( fun @ ( fun @ SV145 @ bool ) @ bool ) @ ( member @ SV145 ) @ ( hAPP @ SV67 @ SV145 @ SV257 @ SV201 ) ) @ SV330 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool @ ( hAPP @ ( fun @ SV67 @ SV145 ) @ ( fun @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ bool ) @ ( member @ ( fun @ SV67 @ SV145 ) ) @ SV257 ) @ ( hAPP @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) @ ( hAPP @ ( fun @ SV67 @ bool ) @ ( fun @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( fun @ ( fun @ SV67 @ SV145 ) @ bool ) ) @ ( pi @ SV67 @ SV145 ) @ SV304 ) @ ( hAPP @ ( fun @ SV145 @ bool ) @ ( fun @ SV67 @ ( fun @ SV145 @ bool ) ) @ ( combk @ ( fun @ SV145 @ bool ) @ SV67 ) @ SV330 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1393,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1394,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1395,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1396,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1397,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1398,plain,
! [SV162: $i,SV86: $i] :
( ( ~ ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1399,plain,
! [SV396: $i,SV384: $i,SV162: $i,SV86: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV384 ) @ SV396 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1400,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i,SV385: $i,SV366: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1401,plain,
! [SV87: $i,SV163: $i,SV262: $i,SV211: $i,SV386: $i,SV367: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1402,plain,
! [SV397: $i,SV368: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV368 ) @ SV397 ) ) )
= $true )
| ( ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SV368 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1403,plain,
! [SV387: $i,SV369: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
!= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV369 ) @ SV387 ) ) )
= $true )
| ( ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SV387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1404,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1405,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1318]) ).
thf(1406,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1407,plain,
! [SV89: $i,SV165: $i] :
( ( ~ ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1408,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1409,plain,
! [SV165: $i,SV89: $i] :
( ( ~ ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1410,plain,
! [SV398: $i,SV388: $i,SV165: $i,SV89: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV388 ) @ SV398 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV398 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1411,plain,
! [SV370: $i,SV347: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV347 ) @ SV370 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV370 ) @ SV347 ) )
= $true )
| ( ( ( ti @ SV90 @ SV347 )
= ( ti @ SV90 @ SV370 ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1412,plain,
! [SV399: $i,SV90: $i] :
( ( ( ! [SY2175: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV399 ) @ SY2175 ) )
| ( ( ti @ SV90 @ SV399 )
!= ( ti @ SV90 @ SY2175 ) ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1413,plain,
! [SV400: $i,SV90: $i] :
( ( ( ! [SY2176: $i] :
( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SY2176 ) @ SV400 ) )
| ( ( ti @ SV90 @ SV400 )
!= ( ti @ SV90 @ SY2176 ) ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1414,plain,
! [SV334: $i,SV91: $i,SV308: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SV334 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SV334 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV334 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1415,plain,
! [SV335: $i,SV309: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV309 ) ) @ SV335 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV309 ) @ SV91 ) ) @ SV335 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV309 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV335 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1416,plain,
! [SV349: $i,SV92: $i] :
( ( ( ( ti @ SV92 @ SV349 )
= ( top_top @ SV92 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV92 @ bool @ ( hAPP @ SV92 @ ( fun @ SV92 @ bool ) @ ( ord_less @ SV92 ) @ SV349 ) @ ( top_top @ SV92 ) ) )
= $false )
| ( ( top @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1417,plain,
! [SV264: $i] :
( ( ( ~ ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1418,plain,
! [SV264: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1419,plain,
! [SV265: $i,SV350: $i,SV401: $i] :
( ( ( ! [SY2177: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SY2177 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV350 @ ( sK14_I @ SY2177 @ SV401 @ SV350 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SY2177 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SV350 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV350 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1420,plain,
! [SV402: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1421,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1422,plain,
! [SV403: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV403 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1423,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1424,plain,
! [SV351: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV351 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1425,plain,
! [SV404: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) @ c ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1426,plain,
! [SV405: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1427,plain,
! [SV352: $i,SV371: $i,SV93: $i] :
( ( ( ( ( ti @ SV93 @ SV371 )
!= ( ti @ SV93 @ SV352 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV371 ) @ SV352 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV352 ) @ SV371 ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1428,plain,
! [SV353: $i,SV372: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV372 ) @ SV353 ) )
= $true )
| ( ( ( ti @ SV93 @ SV372 )
= ( ti @ SV93 @ SV353 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV353 ) @ SV372 ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1429,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1430,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1431,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i,SV389: $i,SV373: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1432,plain,
! [SV95: $i,SV167: $i,SV266: $i,SV213: $i,SV390: $i,SV374: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1433,plain,
! [SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1434,plain,
! [SV267: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1435,plain,
! [SV268: $i,SV354: $i,SV406: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ! [SY2178: $i,SY2179: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
| ~ ! [SY2180: $i,SY2181: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1436,plain,
! [SV407: $i,SV97: $i] :
( ( ( ! [SY2182: $i] :
( ( ( ti @ SV97 @ SV407 )
!= ( ti @ SV97 @ SY2182 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV407 ) @ SY2182 ) ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1437,plain,
! [SV408: $i,SV97: $i] :
( ( ( ! [SY2183: $i] :
( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SY2183 ) @ SV408 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV408 ) @ SY2183 ) ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1438,plain,
! [SV375: $i,SV355: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV355 )
= ( ti @ SV97 @ SV375 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV375 ) @ SV355 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV355 ) @ SV375 ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1439,plain,
! [SV356: $i,SV214: $i,SV376: $i,SV169: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV376 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
= $false )
| ( ( ( ( hAPP @ SV98 @ SV169 @ SV376 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SV376 @ SV356 ) )
| ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SV356 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1440,plain,
! [SV357: $i,SV214: $i,SV377: $i,SV169: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV377 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
= $false )
| ( ( ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SV357 ) )
| ( ( hAPP @ SV98 @ SV169 @ SV377 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SV377 @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1441,plain,
! [SV99: $i,SV170: $i,SV358: $i,SV215: $i,SV378: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1442,plain,
! [SV99: $i,SV170: $i,SV359: $i,SV215: $i,SV379: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1443,plain,
! [SV409: $i,SV391: $i,SV338: $i,SV312: $i,SV101: $i] :
( ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( hAPP @ SV312 @ ( product_prod @ SV101 @ SV312 ) @ ( hAPP @ SV101 @ ( fun @ SV312 @ ( product_prod @ SV101 @ SV312 ) ) @ ( product_Pair @ SV101 @ SV312 ) @ SV391 ) @ SV409 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( product_prod @ SV101 @ SV312 ) @ bool @ SV338 @ ( sK26_X1 @ SV338 @ SV312 @ SV101 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1444,plain,
! [SV393: $i,SV271: $i,SV102: $i,SV380: $i,SV216: $i,SV171: $i] :
( ( ( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SV380 ) )
| ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SV393 ) ) )
= $true )
| ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV380 ) @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1445,plain,
! [SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ! [SY2086: $i] :
( ! [SY2087: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2086 ) @ SY2087 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SY2086 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1354]) ).
thf(1446,plain,
! [SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ! [SY2088: $i,SY2089: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SY2088 ) @ SY2089 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2089 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1447,plain,
! [SV217: $i,SV272: $i,SV394: $i,SV381: $i,SV172: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1448,plain,
! [SV217: $i,SV272: $i,SV395: $i,SV382: $i,SV172: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1449,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1450,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1451,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1452,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1453,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1454,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1455,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1456,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1457,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1458,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1459,plain,
! [SV341: $i,SV361: $i,SV174: $i,SV105: $i] :
( ( ( ~ ! [SY2157: $i,SY2158: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV341 ) ) )
| ~ ! [SY2159: $i,SY2160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV361 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1460,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1461,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1462,plain,
! [SV343: $i,SV175: $i,SV363: $i,SV410: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) )
| ! [SY2184: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2184 ) @ SV363 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SY2184 ) )
| ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SY2184 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1463,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) )
| ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1464,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1465,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
| ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1466,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) )
| ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1467,plain,
! [SV364: $i,SV344: $i,SV108: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1468,plain,
! [SV365: $i,SV345: $i,SV108: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1469,plain,
! [SV273: $i,SV314: $i,SV109: $i,SV178: $i,SV220: $i,SV346: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1470,plain,
! [SV315: $i,SV274: $i] :
( ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV274 @ ( sK1_X_1 @ SV315 @ SV274 ) )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK1_X_1 @ SV315 @ SV274 ) @ SV315 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV274 ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1471,plain,
! [SV316: $i,SV275: $i,SV383: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV383 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV275 @ SV383 )
= ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV383 @ SV316 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV275 ) @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1472,plain,
! [SV325: $i,SV191: $i,SV249: $i,SV298: $i,SV131: $i,SV51: $i] :
( ( ( ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
!= ( ti @ SV131 @ SV191 ) ) )
= $true )
| ( ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SV325 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SV325 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1473,plain,
! [SV299: $i,SV132: $i,SV250: $i,SV326: $i,SV192: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
| ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true )
| ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1474,plain,
! [SV300: $i,SV133: $i,SV251: $i,SV327: $i,SV193: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) )
= $true )
| ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1475,plain,
! [SV162: $i,SV86: $i] :
( ( ! [SY1764: $i,SY1765: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1765 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1764 ) @ SY1765 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1393]) ).
thf(1476,plain,
! [SV162: $i,SV86: $i] :
( ( ! [SY1766: $i,SY1767: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1767 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1766 ) @ SY1767 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1477,plain,
! [SV162: $i,SV86: $i] :
( ( ! [SY1768: $i,SY1769: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY1769 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1768 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1768 ) @ SY1769 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1478,plain,
! [SV162: $i,SV86: $i] :
( ( ! [SY1770: $i,SY1771: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY1771 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SY1770 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1770 ) @ SY1771 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1479,plain,
! [SV162: $i,SV86: $i] :
( ( ! [SY1772: $i,SY1773: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1772 ) @ SY1773 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY1773 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1480,plain,
! [SV162: $i,SV86: $i] :
( ( ! [SY1774: $i,SY1775: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SY1774 ) @ SY1775 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY1775 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1481,plain,
! [SV396: $i,SV384: $i,SV162: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV384 ) @ SV396 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1482,plain,
! [SV385: $i,SV366: $i,SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1483,plain,
! [SV386: $i,SV367: $i,SV87: $i,SV163: $i,SV262: $i,SV211: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1484,plain,
! [SV397: $i,SV368: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV368 ) @ SV397 ) )
= $false )
| ( ( ( ti @ SV164 @ SV212 )
= ( ti @ SV164 @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1485,plain,
! [SV387: $i,SV369: $i,SV263: $i,SV212: $i,SV164: $i,SV88: $i] :
( ( ( ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV212 ) @ SV263 )
= ( hAPP @ SV88 @ ( product_prod @ SV164 @ SV88 ) @ ( hAPP @ SV164 @ ( fun @ SV88 @ ( product_prod @ SV164 @ SV88 ) ) @ ( product_Pair @ SV164 @ SV88 ) @ SV369 ) @ SV387 ) )
= $false )
| ( ( ( ti @ SV88 @ SV263 )
= ( ti @ SV88 @ SV387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1486,plain,
! [SV89: $i,SV165: $i] :
( ( ! [SY1790: $i,SY1791: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1791 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1790 ) @ SY1791 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1487,plain,
! [SV89: $i,SV165: $i] :
( ( ! [SY1792: $i,SY1793: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1793 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1792 ) @ SY1793 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1488,plain,
! [SV89: $i,SV165: $i] :
( ( ! [SY1794: $i,SY1795: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY1795 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1794 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1794 ) @ SY1795 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1489,plain,
! [SV89: $i,SV165: $i] :
( ( ! [SY1796: $i,SY1797: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY1797 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SY1796 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1796 ) @ SY1797 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1407]) ).
thf(1490,plain,
! [SV165: $i,SV89: $i] :
( ( ! [SY1798: $i,SY1799: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1798 ) @ SY1799 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY1799 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1491,plain,
! [SV165: $i,SV89: $i] :
( ( ! [SY1800: $i,SY1801: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SY1800 ) @ SY1801 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY1801 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1492,plain,
! [SV398: $i,SV388: $i,SV165: $i,SV89: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV388 ) @ SV398 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV398 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV388 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1493,plain,
! [SV411: $i,SV399: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV399 ) @ SV411 ) )
| ( ( ti @ SV90 @ SV399 )
!= ( ti @ SV90 @ SV411 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1494,plain,
! [SV400: $i,SV412: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV412 ) @ SV400 ) )
| ( ( ti @ SV90 @ SV400 )
!= ( ti @ SV90 @ SV412 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1495,plain,
! [SV334: $i,SV91: $i,SV308: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SV334 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SV334 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV334 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1496,plain,
! [SV264: $i] :
( ( ( ! [SY2068: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SY2068 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1497,plain,
! [SV264: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1498,plain,
! [SV265: $i,SV350: $i,SV413: $i,SV401: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SV413 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV350 @ ( sK14_I @ SV413 @ SV401 @ SV350 @ SV265 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SV413 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SV350 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV350 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1499,plain,
! [SV402: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1500,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1501,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1502,plain,
! [SV403: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV403 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1503,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1504,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1505,plain,
! [SV351: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV351 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV351 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1506,plain,
! [SV404: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1507,plain,
! [SV405: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1508,plain,
! [SV352: $i,SV371: $i,SV93: $i] :
( ( ( ( ti @ SV93 @ SV371 )
= ( ti @ SV93 @ SV352 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV371 ) @ SV352 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV352 ) @ SV371 ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1509,plain,
! [SV94: $i,SV166: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
!= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1510,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1511,plain,
! [SV95: $i,SV167: $i,SV389: $i,SV373: $i,SV266: $i,SV213: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1512,plain,
! [SV95: $i,SV167: $i,SV390: $i,SV374: $i,SV266: $i,SV213: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1513,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ ( sK21_SY1318 @ SV267 ) ) @ arrow_1834574746e_Prof ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1514,plain,
! [SV267: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1515,plain,
! [SV268: $i,SV354: $i,SV406: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2178: $i,SY2179: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
| ~ ! [SY2180: $i,SY2181: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1516,plain,
! [SV414: $i,SV407: $i,SV97: $i] :
( ( ( ( ( ti @ SV97 @ SV407 )
!= ( ti @ SV97 @ SV414 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV407 ) @ SV414 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1517,plain,
! [SV408: $i,SV415: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV415 ) @ SV408 ) )
| ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV408 ) @ SV415 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1518,plain,
! [SV356: $i,SV214: $i,SV376: $i,SV169: $i,SV98: $i] :
( ( ( ( ( hAPP @ SV98 @ SV169 @ SV376 @ SV214 )
!= ( hAPP @ SV98 @ SV169 @ SV376 @ SV356 ) ) )
= $true )
| ( ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SV356 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV376 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1519,plain,
! [SV377: $i,SV169: $i,SV357: $i,SV214: $i,SV98: $i] :
( ( ( ( ( ti @ SV98 @ SV214 )
!= ( ti @ SV98 @ SV357 ) ) )
= $true )
| ( ( ( hAPP @ SV98 @ SV169 @ SV377 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SV377 @ SV357 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV377 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1520,plain,
! [SV378: $i,SV99: $i,SV170: $i,SV215: $i,SV358: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1521,plain,
! [SV379: $i,SV99: $i,SV170: $i,SV215: $i,SV359: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1522,plain,
! [SV393: $i,SV271: $i,SV102: $i,SV380: $i,SV216: $i,SV171: $i] :
( ( ( ( ( ti @ SV171 @ SV216 )
!= ( ti @ SV171 @ SV380 ) ) )
= $true )
| ( ( ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SV393 ) ) )
= $true )
| ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV380 ) @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1523,plain,
! [SV416: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ! [SY2185: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV416 ) @ SY2185 ) )
| ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1524,plain,
! [SV417: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ! [SY2186: $i] :
( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV417 ) @ SY2186 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SY2186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1525,plain,
! [SV217: $i,SV272: $i,SV394: $i,SV381: $i,SV172: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1526,plain,
! [SV217: $i,SV272: $i,SV395: $i,SV382: $i,SV172: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1527,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1528,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1449]) ).
thf(1529,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1530,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1531,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1532,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1533,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1534,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1535,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1536,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1537,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1538,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1539,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1540,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1541,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1542,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1543,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1544,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1545,plain,
! [SV341: $i,SV361: $i,SV174: $i,SV105: $i] :
( ( ( ~ ! [SY2157: $i,SY2158: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV341 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1546,plain,
! [SV361: $i,SV341: $i,SV174: $i,SV105: $i] :
( ( ( ~ ! [SY2159: $i,SY2160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV361 ) ) ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1547,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1548,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1549,plain,
! [SV343: $i,SV175: $i,SV363: $i,SV410: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) ) )
= $true )
| ( ( ! [SY2184: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2184 ) @ SV363 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SY2184 ) )
| ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SY2184 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1550,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1551,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1552,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1553,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1554,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1555,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1556,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1466]) ).
thf(1557,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1466]) ).
thf(1558,plain,
! [SV177: $i,SV364: $i,SV344: $i,SV108: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1559,plain,
! [SV177: $i,SV365: $i,SV345: $i,SV108: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1560,plain,
! [SV220: $i,SV273: $i,SV346: $i,SV314: $i,SV109: $i,SV178: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1561,plain,
! [SV325: $i,SV191: $i,SV249: $i,SV298: $i,SV131: $i,SV51: $i] :
( ( ( ( hAPP @ SV51 @ SV131 @ SV298 @ SV249 )
= ( ti @ SV131 @ SV191 ) )
= $false )
| ( ( ( hAPP @ SV131 @ SV51 @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) @ ( hAPP @ ( fun @ SV51 @ bool ) @ ( fun @ ( fun @ SV51 @ SV131 ) @ ( fun @ SV131 @ SV51 ) ) @ ( hilbert_inv_into @ SV51 @ SV131 ) @ SV325 ) @ SV298 ) @ SV191 )
= ( ti @ SV51 @ SV249 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ SV51 @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( member @ SV51 ) @ SV249 ) @ SV325 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV51 @ bool ) @ bool @ ( hAPP @ ( fun @ SV51 @ SV131 ) @ ( fun @ ( fun @ SV51 @ bool ) @ bool ) @ ( inj_on @ SV51 @ SV131 ) @ SV298 ) @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1562,plain,
! [SV192: $i,SV299: $i,SV132: $i,SV326: $i,SV250: $i,SV52: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) ) )
= $true )
| ( ( ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
= $false )
| ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1563,plain,
! [SV300: $i,SV133: $i,SV251: $i,SV327: $i,SV193: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
| ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) ) )
= $true )
| ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1564,plain,
! [SV418: $i,SV162: $i,SV86: $i] :
( ( ! [SY2187: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY2187 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY2187 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY2187 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV418 ) @ SY2187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1565,plain,
! [SV419: $i,SV162: $i,SV86: $i] :
( ( ! [SY2188: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY2188 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY2188 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV419 ) @ SY2188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1566,plain,
! [SV420: $i,SV162: $i,SV86: $i] :
( ( ! [SY2189: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY2189 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SY2189 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV420 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV420 ) @ SY2189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1567,plain,
! [SV421: $i,SV162: $i,SV86: $i] :
( ( ! [SY2190: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SY2190 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV421 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV421 ) @ SY2190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1568,plain,
! [SV422: $i,SV162: $i,SV86: $i] :
( ( ! [SY2191: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV422 ) @ SY2191 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SY2191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1569,plain,
! [SV423: $i,SV162: $i,SV86: $i] :
( ( ! [SY2192: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV423 ) @ SY2192 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SY2192 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1570,plain,
! [SV396: $i,SV384: $i,SV162: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV384 ) @ SV396 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV396 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV384 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1571,plain,
! [SV211: $i,SV262: $i,SV385: $i,SV366: $i,SV87: $i,SV163: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1572,plain,
! [SV211: $i,SV262: $i,SV386: $i,SV367: $i,SV87: $i,SV163: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1483]) ).
thf(1573,plain,
! [SV424: $i,SV89: $i,SV165: $i] :
( ( ! [SY2193: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY2193 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY2193 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY2193 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV424 ) @ SY2193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1574,plain,
! [SV425: $i,SV89: $i,SV165: $i] :
( ( ! [SY2194: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY2194 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY2194 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV425 ) @ SY2194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1575,plain,
! [SV426: $i,SV89: $i,SV165: $i] :
( ( ! [SY2195: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY2195 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SY2195 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV426 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV426 ) @ SY2195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1576,plain,
! [SV427: $i,SV89: $i,SV165: $i] :
( ( ! [SY2196: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SY2196 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV427 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV427 ) @ SY2196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1577,plain,
! [SV428: $i,SV165: $i,SV89: $i] :
( ( ! [SY2197: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV428 ) @ SY2197 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SY2197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1578,plain,
! [SV429: $i,SV165: $i,SV89: $i] :
( ( ! [SY2198: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV429 ) @ SY2198 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SY2198 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1579,plain,
! [SV398: $i,SV388: $i,SV165: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV388 ) @ SV398 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV398 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV388 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1580,plain,
! [SV411: $i,SV399: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV399 ) @ SV411 ) ) )
= $true )
| ( ( ( ( ti @ SV90 @ SV399 )
!= ( ti @ SV90 @ SV411 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1581,plain,
! [SV400: $i,SV412: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV412 ) @ SV400 ) ) )
= $true )
| ( ( ( ( ti @ SV90 @ SV400 )
!= ( ti @ SV90 @ SV412 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1582,plain,
! [SV334: $i,SV308: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV91 ) @ SV308 ) ) @ SV334 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV308 ) @ SV91 ) ) @ SV334 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV91 )
= ( ti @ arrow_1212486748le_alt @ SV308 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV334 ) @ arrow_638930832le_Lin ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1583,plain,
! [SV430: $i,SV264: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK15_X_1 @ SV264 ) @ SV430 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1584,plain,
! [SV264: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK16_SY1312 @ SV264 ) ) @ ( sK17_SY1315 @ SV264 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV264 @ ( sK15_X_1 @ SV264 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1585,plain,
! [SV265: $i,SV350: $i,SV413: $i,SV401: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SV413 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV350 @ ( sK14_I @ SV413 @ SV401 @ SV350 @ SV265 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SV413 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SV350 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV350 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1586,plain,
! [SV402: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1587,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1588,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1589,plain,
! [SV403: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV403 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1590,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1591,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1592,plain,
! [SV404: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1593,plain,
! [SV405: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1594,plain,
! [SV352: $i,SV371: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV371 ) @ SV352 ) )
= $false )
| ( ( ( ti @ SV93 @ SV371 )
= ( ti @ SV93 @ SV352 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV93 @ bool @ ( hAPP @ SV93 @ ( fun @ SV93 @ bool ) @ ( ord_less @ SV93 ) @ SV352 ) @ SV371 ) )
= $true )
| ( ( linorder @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1595,plain,
! [SV94: $i,SV166: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ ( sK4_SY1306 @ SV166 @ SV94 ) )
= ( ti @ arrow_1212486748le_alt @ ( sK5_SY1308 @ SV166 @ SV94 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1596,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
| ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1597,plain,
! [SV95: $i,SV167: $i,SV213: $i,SV389: $i,SV266: $i,SV373: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1598,plain,
! [SV95: $i,SV167: $i,SV213: $i,SV390: $i,SV266: $i,SV374: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1599,plain,
! [SV267: $i] :
( ( ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
| ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1600,plain,
! [SV268: $i,SV354: $i,SV406: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ! [SY2178: $i,SY2179: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
| ~ ! [SY2180: $i,SY2181: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1601,plain,
! [SV414: $i,SV407: $i,SV97: $i] :
( ( ( ( ( ti @ SV97 @ SV407 )
!= ( ti @ SV97 @ SV414 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV407 ) @ SV414 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1602,plain,
! [SV408: $i,SV415: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV415 ) @ SV408 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV408 ) @ SV415 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1603,plain,
! [SV356: $i,SV214: $i,SV376: $i,SV169: $i,SV98: $i] :
( ( ( ( hAPP @ SV98 @ SV169 @ SV376 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SV376 @ SV356 ) )
= $false )
| ( ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SV356 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV376 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1604,plain,
! [SV377: $i,SV169: $i,SV357: $i,SV214: $i,SV98: $i] :
( ( ( ( ti @ SV98 @ SV214 )
= ( ti @ SV98 @ SV357 ) )
= $false )
| ( ( ( hAPP @ SV98 @ SV169 @ SV377 @ SV214 )
= ( hAPP @ SV98 @ SV169 @ SV377 @ SV357 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV98 @ bool ) @ bool @ ( hAPP @ ( fun @ SV98 @ SV169 ) @ ( fun @ ( fun @ SV98 @ bool ) @ bool ) @ ( inj_on @ SV98 @ SV169 ) @ SV377 ) @ ( top_top @ ( fun @ SV98 @ bool ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1605,plain,
! [SV215: $i,SV378: $i,SV358: $i,SV99: $i,SV170: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1606,plain,
! [SV215: $i,SV379: $i,SV359: $i,SV99: $i,SV170: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1607,plain,
! [SV393: $i,SV271: $i,SV102: $i,SV380: $i,SV216: $i,SV171: $i] :
( ( ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SV380 ) )
= $false )
| ( ( ( ( ti @ SV102 @ SV271 )
!= ( ti @ SV102 @ SV393 ) ) )
= $true )
| ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV380 ) @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1608,plain,
! [SV416: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ( ! [SY2185: $i] :
( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV416 ) @ SY2185 ) ) )
= $true )
| ( ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1609,plain,
! [SV431: $i,SV417: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV417 ) @ SV431 ) )
| ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1610,plain,
! [SV381: $i,SV172: $i,SV217: $i,SV394: $i,SV272: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1611,plain,
! [SV382: $i,SV172: $i,SV217: $i,SV395: $i,SV272: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1612,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1613,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1614,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1615,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1616,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1617,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1532]) ).
thf(1618,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1619,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1620,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1621,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1622,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1623,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1624,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1625,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1626,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1627,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1628,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1629,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1630,plain,
! [SV341: $i,SV361: $i,SV174: $i,SV105: $i] :
( ( ( ! [SY2157: $i,SY2158: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2157 ) @ SY2158 ) ) @ SV341 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1631,plain,
! [SV361: $i,SV341: $i,SV174: $i,SV105: $i] :
( ( ( ! [SY2159: $i,SY2160: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SY2159 ) @ SY2160 ) ) @ SV361 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1632,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
| ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1633,plain,
! [SV343: $i,SV175: $i,SV363: $i,SV410: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) )
= $false )
| ( ( ! [SY2184: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SY2184 ) @ SV363 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SY2184 ) )
| ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SY2184 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1634,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1973: $i,SY1974: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1973 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1974 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1973 ) @ SY1974 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1635,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1975: $i,SY1976: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1975 )
= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1975 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1976 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1975 ) @ SY1976 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1636,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1637,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1553]) ).
thf(1638,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY2001: $i,SY2002: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2001 )
= ( ti @ arrow_1212486748le_alt @ SY2002 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2001 ) @ SY2002 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1639,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY2003: $i,SY2004: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2003 )
= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2003 ) @ SY2004 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2004 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2003 ) @ SV176 ) ) @ SV219 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1640,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY2005: $i,SY2006: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2005 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2005 ) @ SY2006 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2006 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2005 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY2005 ) ) @ SV219 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1556]) ).
thf(1641,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY2007: $i,SY2008: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY2007 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY2007 ) @ SY2008 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2008 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1642,plain,
! [SV177: $i,SV364: $i,SV344: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1643,plain,
! [SV177: $i,SV365: $i,SV345: $i,SV108: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1644,plain,
! [SV220: $i,SV273: $i,SV346: $i,SV314: $i,SV109: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1645,plain,
! [SV192: $i,SV299: $i,SV132: $i,SV326: $i,SV250: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
= $false )
| ( ( ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
!= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
= $false )
| ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1646,plain,
! [SV300: $i,SV133: $i,SV193: $i,SV327: $i,SV251: $i,SV53: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) ) )
= $true )
| ( ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
= $false )
| ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1647,plain,
! [SV418: $i,SV162: $i,SV432: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV432 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV418 ) @ SV432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1648,plain,
! [SV419: $i,SV162: $i,SV433: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV433 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV433 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV419 ) @ SV433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1649,plain,
! [SV420: $i,SV162: $i,SV434: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV420 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV420 ) @ SV434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1650,plain,
! [SV421: $i,SV162: $i,SV435: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV435 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV421 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV421 ) @ SV435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1651,plain,
! [SV436: $i,SV422: $i,SV162: $i,SV86: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV422 ) @ SV436 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1652,plain,
! [SV437: $i,SV423: $i,SV162: $i,SV86: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV423 ) @ SV437 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV437 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1653,plain,
! [SV384: $i,SV86: $i,SV396: $i,SV162: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV396 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV384 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV384 ) @ SV396 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1654,plain,
! [SV211: $i,SV262: $i,SV385: $i,SV366: $i,SV87: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1655,plain,
! [SV211: $i,SV262: $i,SV386: $i,SV367: $i,SV87: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1656,plain,
! [SV424: $i,SV89: $i,SV438: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV438 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV424 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1657,plain,
! [SV425: $i,SV89: $i,SV439: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV439 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV439 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV425 ) @ SV439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1658,plain,
! [SV426: $i,SV89: $i,SV440: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV426 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV426 ) @ SV440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1659,plain,
! [SV427: $i,SV89: $i,SV441: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV441 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV427 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV427 ) @ SV441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1660,plain,
! [SV442: $i,SV428: $i,SV165: $i,SV89: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV428 ) @ SV442 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1661,plain,
! [SV443: $i,SV429: $i,SV165: $i,SV89: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV429 ) @ SV443 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV443 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1662,plain,
! [SV388: $i,SV165: $i,SV398: $i,SV89: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV398 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV388 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV388 ) @ SV398 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1663,plain,
! [SV411: $i,SV399: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV399 ) @ SV411 ) )
= $false )
| ( ( ( ( ti @ SV90 @ SV399 )
!= ( ti @ SV90 @ SV411 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1664,plain,
! [SV400: $i,SV412: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV412 ) @ SV400 ) )
= $false )
| ( ( ( ( ti @ SV90 @ SV400 )
!= ( ti @ SV90 @ SV412 ) ) )
= $true )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1665,plain,
! [SV265: $i,SV350: $i,SV413: $i,SV401: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SV413 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV350 @ ( sK14_I @ SV413 @ SV401 @ SV350 @ SV265 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV401 ) @ SV413 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV265 @ SV350 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV350 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_1932713123nimity @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1666,plain,
! [SV402: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV402 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV402 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1667,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1668,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1669,plain,
! [SV403: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV403 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1670,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1671,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1672,plain,
! [SV404: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1673,plain,
! [SV405: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1674,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1675,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1596]) ).
thf(1676,plain,
! [SV266: $i,SV373: $i,SV95: $i,SV167: $i,SV213: $i,SV389: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1677,plain,
! [SV266: $i,SV374: $i,SV95: $i,SV167: $i,SV213: $i,SV390: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1678,plain,
! [SV267: $i] :
( ( ( ~ ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1679,plain,
! [SV267: $i] :
( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1599]) ).
thf(1680,plain,
! [SV268: $i,SV406: $i,SV354: $i] :
( ( ( ~ ! [SY2178: $i,SY2179: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
| ~ ! [SY2180: $i,SY2181: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1681,plain,
! [SV414: $i,SV407: $i,SV97: $i] :
( ( ( ( ti @ SV97 @ SV407 )
= ( ti @ SV97 @ SV414 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV407 ) @ SV414 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1682,plain,
! [SV408: $i,SV415: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV415 ) @ SV408 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV408 ) @ SV415 ) ) )
= $true )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1683,plain,
! [SV215: $i,SV378: $i,SV358: $i,SV99: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1684,plain,
! [SV215: $i,SV379: $i,SV359: $i,SV99: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1685,plain,
! [SV380: $i,SV216: $i,SV171: $i,SV393: $i,SV271: $i,SV102: $i] :
( ( ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SV393 ) )
= $false )
| ( ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SV380 ) )
= $false )
| ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV380 ) @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1686,plain,
! [SV444: $i,SV416: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV416 ) @ SV444 ) ) )
= $true )
| ( ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1687,plain,
! [SV431: $i,SV417: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
!= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV417 ) @ SV431 ) ) )
= $true )
| ( ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1688,plain,
! [SV381: $i,SV172: $i,SV217: $i,SV394: $i,SV272: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1689,plain,
! [SV382: $i,SV172: $i,SV217: $i,SV395: $i,SV272: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
| ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1690,plain,
! [SV445: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1691,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1692,plain,
! [SV446: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV446 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1693,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1694,plain,
! [SV447: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1695,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1696,plain,
! [SV448: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV448 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1697,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1698,plain,
! [SV449: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV449 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1699,plain,
! [SV450: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV450 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1700,plain,
! [SV451: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV451 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1701,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1702,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1703,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1704,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1705,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1706,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1707,plain,
! [SV341: $i,SV361: $i,SV452: $i,SV174: $i,SV105: $i] :
( ( ( ! [SY2199: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SY2199 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SY2199 ) ) @ SV341 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1708,plain,
! [SV361: $i,SV341: $i,SV453: $i,SV174: $i,SV105: $i] :
( ( ( ! [SY2200: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SY2200 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SY2200 ) ) @ SV361 ) ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1709,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1710,plain,
! [SV362: $i,SV342: $i,SV175: $i,SV106: $i] :
( ( ( ~ ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1711,plain,
! [SV410: $i,SV343: $i,SV175: $i,SV363: $i,SV454: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV454 ) @ SV363 ) )
| ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SV454 ) )
| ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SV454 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1712,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV455: $i] :
( ( ! [SY2201: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SY2201 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2201 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2201 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SY2201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1713,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV456: $i] :
( ( ! [SY2202: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SY2202 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2202 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SY2202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1714,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1715,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1716,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV457: $i] :
( ( ! [SY2203: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SY2203 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SY2203 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1717,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV458: $i] :
( ( ! [SY2204: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SY2204 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SY2204 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY2204 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1718,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV459: $i] :
( ( ! [SY2205: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SY2205 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SY2205 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2205 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2205 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1719,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV460: $i] :
( ( ! [SY2206: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SY2206 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SY2206 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2206 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2206 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1720,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1721,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1722,plain,
! [SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i,SV109: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1723,plain,
! [SV326: $i,SV250: $i,SV192: $i,SV299: $i,SV132: $i,SV52: $i] :
( ( ( ( hAPP @ SV52 @ SV132 @ SV299 @ SV192 )
= ( hAPP @ SV52 @ SV132 @ SV299 @ SV250 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV250 ) @ SV326 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ SV52 @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( member @ SV52 ) @ SV192 ) @ SV326 ) )
= $false )
| ( ( ( ti @ SV52 @ SV192 )
= ( ti @ SV52 @ SV250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV52 @ bool ) @ bool @ ( hAPP @ ( fun @ SV52 @ SV132 ) @ ( fun @ ( fun @ SV52 @ bool ) @ bool ) @ ( inj_on @ SV52 @ SV132 ) @ SV299 ) @ SV326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1724,plain,
! [SV300: $i,SV133: $i,SV193: $i,SV327: $i,SV251: $i,SV53: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV251 ) @ SV327 ) )
= $false )
| ( ( ( ti @ SV53 @ SV193 )
= ( ti @ SV53 @ SV251 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ SV53 @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( member @ SV53 ) @ SV193 ) @ SV327 ) )
= $false )
| ( ( ( hAPP @ SV53 @ SV133 @ SV300 @ SV193 )
= ( hAPP @ SV53 @ SV133 @ SV300 @ SV251 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV53 @ bool ) @ bool @ ( hAPP @ ( fun @ SV53 @ SV133 ) @ ( fun @ ( fun @ SV53 @ bool ) @ bool ) @ ( inj_on @ SV53 @ SV133 ) @ SV300 ) @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1725,plain,
! [SV418: $i,SV162: $i,SV432: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV432 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV418 ) @ SV432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1726,plain,
! [SV419: $i,SV162: $i,SV433: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV433 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV433 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV419 ) @ SV433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1727,plain,
! [SV420: $i,SV162: $i,SV434: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV420 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV420 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1728,plain,
! [SV421: $i,SV162: $i,SV435: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV435 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV421 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV421 ) @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1729,plain,
! [SV436: $i,SV422: $i,SV162: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV422 ) @ SV436 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1730,plain,
! [SV437: $i,SV423: $i,SV162: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV423 ) @ SV437 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV437 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1731,plain,
! [SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i,SV87: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1732,plain,
! [SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i,SV87: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1733,plain,
! [SV424: $i,SV89: $i,SV438: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV424 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1734,plain,
! [SV425: $i,SV89: $i,SV439: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV439 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV439 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV425 ) @ SV439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1735,plain,
! [SV426: $i,SV89: $i,SV440: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV426 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV426 ) @ SV440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1736,plain,
! [SV427: $i,SV89: $i,SV441: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV441 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV427 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV427 ) @ SV441 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1737,plain,
! [SV442: $i,SV428: $i,SV165: $i,SV89: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV428 ) @ SV442 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1738,plain,
! [SV443: $i,SV429: $i,SV165: $i,SV89: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV429 ) @ SV443 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV443 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1739,plain,
! [SV411: $i,SV399: $i,SV90: $i] :
( ( ( ( ti @ SV90 @ SV399 )
= ( ti @ SV90 @ SV411 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV399 ) @ SV411 ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1740,plain,
! [SV412: $i,SV400: $i,SV90: $i] :
( ( ( ( ti @ SV90 @ SV400 )
= ( ti @ SV90 @ SV412 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV90 @ bool @ ( hAPP @ SV90 @ ( fun @ SV90 @ bool ) @ ( ord_less @ SV90 ) @ SV412 ) @ SV400 ) )
= $false )
| ( ( linorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1741,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1742,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1743,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1744,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1745,plain,
! [SV403: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV403 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV403 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1746,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1747,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1748,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1749,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1750,plain,
! [SV404: $i] :
( ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1751,plain,
! [SV405: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV405 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV405 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1752,plain,
! [SV94: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK3_X_1 @ SV166 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1753,plain,
! [SV94: $i,SV166: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1754,plain,
! [SV213: $i,SV266: $i,SV389: $i,SV373: $i,SV95: $i,SV167: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1755,plain,
! [SV213: $i,SV266: $i,SV390: $i,SV374: $i,SV95: $i,SV167: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1756,plain,
! [SV267: $i] :
( ( ( ~ ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1757,plain,
! [SV267: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1758,plain,
! [SV268: $i,SV406: $i,SV354: $i] :
( ( ( ~ ! [SY2178: $i,SY2179: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1680]) ).
thf(1759,plain,
! [SV268: $i,SV406: $i,SV354: $i] :
( ( ( ~ ! [SY2180: $i,SY2181: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1680]) ).
thf(1760,plain,
! [SV414: $i,SV407: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV407 ) @ SV414 ) )
= $false )
| ( ( ( ti @ SV97 @ SV407 )
= ( ti @ SV97 @ SV414 ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1761,plain,
! [SV415: $i,SV408: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV408 ) @ SV415 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV97 @ bool @ ( hAPP @ SV97 @ ( fun @ SV97 @ bool ) @ ( ord_less @ SV97 ) @ SV415 ) @ SV408 ) )
= $false )
| ( ( linorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1762,plain,
! [SV215: $i,SV170: $i,SV378: $i,SV358: $i,SV99: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1763,plain,
! [SV215: $i,SV170: $i,SV379: $i,SV359: $i,SV99: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1764,plain,
! [SV444: $i,SV416: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV416 ) @ SV444 ) )
= $false )
| ( ( ( ti @ SV171 @ SV216 )
= ( ti @ SV171 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1765,plain,
! [SV431: $i,SV417: $i,SV271: $i,SV216: $i,SV171: $i,SV102: $i] :
( ( ( ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV216 ) @ SV271 )
= ( hAPP @ SV102 @ ( product_prod @ SV171 @ SV102 ) @ ( hAPP @ SV171 @ ( fun @ SV102 @ ( product_prod @ SV171 @ SV102 ) ) @ ( product_Pair @ SV171 @ SV102 ) @ SV417 ) @ SV431 ) )
= $false )
| ( ( ( ti @ SV102 @ SV271 )
= ( ti @ SV102 @ SV431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1766,plain,
! [SV272: $i,SV381: $i,SV172: $i,SV394: $i,SV217: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) ) )
= $true )
| ( ( ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1767,plain,
! [SV382: $i,SV172: $i,SV272: $i,SV395: $i,SV217: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) ) )
= $true )
| ( ( ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1768,plain,
! [SV445: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1769,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1770,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1771,plain,
! [SV446: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV446 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1772,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1773,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1774,plain,
! [SV447: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1775,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1776,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1777,plain,
! [SV448: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV448 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1778,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1779,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1780,plain,
! [SV449: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV449 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1781,plain,
! [SV450: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV450 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1782,plain,
! [SV451: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV451 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(1783,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1784,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1785,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1786,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1787,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1788,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1789,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1790,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1791,plain,
( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1792,plain,
! [SV340: $i,SV360: $i,SV174: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV340 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ ( sK12_X_1 @ SV360 @ SV340 @ SV174 @ SV105 ) ) @ ( sK13_SY1311 @ SV360 @ SV340 @ SV174 @ SV105 ) ) ) @ SV360 ) )
= $false )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV360 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1793,plain,
! [SV341: $i,SV361: $i,SV461: $i,SV452: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SV461 ) ) @ SV361 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SV461 ) ) @ SV341 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(1794,plain,
! [SV361: $i,SV341: $i,SV462: $i,SV453: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SV462 ) ) @ SV341 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SV462 ) ) @ SV361 ) ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1795,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) @ SV362 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1796,plain,
! [SV362: $i,SV342: $i,SV175: $i,SV106: $i] :
( ( ( ~ ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1797,plain,
! [SV410: $i,SV343: $i,SV175: $i,SV363: $i,SV454: $i,SV106: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV454 ) @ SV363 ) ) )
= $true )
| ( ( ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SV454 ) )
| ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SV454 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1798,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV463: $i,SV455: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1799,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV464: $i,SV456: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1800,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1801,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1802,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1803,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1804,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV465: $i,SV457: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SV465 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SV465 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1805,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV466: $i,SV458: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV466 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(1806,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV467: $i,SV459: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1807,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV468: $i,SV460: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(1808,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1809,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1810,plain,
! [SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i,SV109: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1811,plain,
! [SV418: $i,SV162: $i,SV432: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV432 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV418 ) @ SV432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1812,plain,
! [SV419: $i,SV162: $i,SV433: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV433 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV433 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV419 ) @ SV433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1813,plain,
! [SV420: $i,SV162: $i,SV434: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV420 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV420 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1814,plain,
! [SV421: $i,SV162: $i,SV435: $i,SV86: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV435 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV421 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV421 ) @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(1815,plain,
! [SV436: $i,SV422: $i,SV162: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV422 ) @ SV436 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV436 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1816,plain,
! [SV437: $i,SV423: $i,SV162: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV423 ) @ SV437 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV437 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1817,plain,
! [SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i,SV87: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1818,plain,
! [SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i,SV87: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1819,plain,
! [SV424: $i,SV89: $i,SV438: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV424 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1820,plain,
! [SV425: $i,SV89: $i,SV439: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV439 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV439 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV425 ) @ SV439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1821,plain,
! [SV426: $i,SV89: $i,SV440: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV426 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV426 ) @ SV440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1822,plain,
! [SV427: $i,SV89: $i,SV441: $i,SV165: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV441 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV427 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV427 ) @ SV441 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1823,plain,
! [SV442: $i,SV428: $i,SV165: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV428 ) @ SV442 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
!= ( ti @ arrow_1212486748le_alt @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1824,plain,
! [SV443: $i,SV429: $i,SV165: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV429 ) @ SV443 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV443 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(1825,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1741]) ).
thf(1826,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1827,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1828,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(1829,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1830,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1831,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1832,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1833,plain,
! [SV404: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV404 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV404 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1834,plain,
! [SV94: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK4_SY1306 @ SV166 @ SV94 ) ) @ ( sK5_SY1308 @ SV166 @ SV94 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV166 @ ( sK3_X_1 @ SV166 @ SV94 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ arrow_1384031255e_indi @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ arrow_1384031255e_indi @ bool ) @ arrow_1990387629ctator @ SV166 ) @ SV94 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV166 ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) ) @ ( pi @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_1834574746e_Prof ) @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_638930832le_Lin ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1835,plain,
! [SV213: $i,SV266: $i,SV389: $i,SV373: $i,SV95: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1836,plain,
! [SV213: $i,SV266: $i,SV390: $i,SV374: $i,SV95: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1837,plain,
! [SV267: $i] :
( ( ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) )
| ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1838,plain,
! [SV267: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1839,plain,
! [SV268: $i,SV406: $i,SV354: $i] :
( ( ( ! [SY2178: $i,SY2179: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2179 @ SY2178 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2178 ) @ SY2179 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(1840,plain,
! [SV268: $i,SV406: $i,SV354: $i] :
( ( ( ! [SY2180: $i,SY2181: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2181 @ SY2180 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY2180 ) @ SY2181 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1841,plain,
! [SV215: $i,SV170: $i,SV378: $i,SV358: $i,SV99: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1842,plain,
! [SV215: $i,SV170: $i,SV379: $i,SV359: $i,SV99: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1843,plain,
! [SV272: $i,SV381: $i,SV172: $i,SV394: $i,SV217: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
= $false )
| ( ( ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
| ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1844,plain,
! [SV382: $i,SV172: $i,SV272: $i,SV395: $i,SV217: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
= $false )
| ( ( ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) )
| ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1845,plain,
! [SV445: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1846,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1847,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1770]) ).
thf(1848,plain,
! [SV446: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV446 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1849,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1850,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1851,plain,
! [SV447: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1852,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1853,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1854,plain,
! [SV448: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV448 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1855,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1856,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1857,plain,
! [SV449: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV449 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1858,plain,
! [SV450: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV450 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(1859,plain,
! [SV451: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV451 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1860,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1861,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1862,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1863,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1864,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1865,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1866,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1867,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1868,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1869,plain,
! [SV341: $i,SV361: $i,SV461: $i,SV452: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SV461 ) ) @ SV361 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SV461 ) ) @ SV341 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1870,plain,
! [SV361: $i,SV341: $i,SV462: $i,SV453: $i,SV174: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SV462 ) ) @ SV341 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SV462 ) ) @ SV361 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1871,plain,
! [SV362: $i,SV342: $i,SV175: $i,SV106: $i] :
( ( ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
| ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1872,plain,
! [SV410: $i,SV343: $i,SV175: $i,SV363: $i,SV454: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV454 ) @ SV363 ) )
= $false )
| ( ( ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SV454 ) )
| ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SV454 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1873,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV463: $i,SV455: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1874,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV464: $i,SV456: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1875,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1876,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1877,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1878,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1879,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV465: $i,SV457: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SV465 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SV465 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1880,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV466: $i,SV458: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV466 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(1881,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV467: $i,SV459: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1806]) ).
thf(1882,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV468: $i,SV460: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1883,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1884,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1885,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1809]) ).
thf(1886,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1809]) ).
thf(1887,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1888,plain,
! [SV418: $i,SV162: $i,SV432: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV432 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV418 ) @ SV432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(1889,plain,
! [SV419: $i,SV162: $i,SV433: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV433 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV433 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV419 ) @ SV433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1890,plain,
! [SV420: $i,SV162: $i,SV434: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV420 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV420 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1891,plain,
! [SV421: $i,SV162: $i,SV435: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV435 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV421 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV421 ) @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1892,plain,
! [SV422: $i,SV162: $i,SV436: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV436 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV422 ) @ SV436 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1893,plain,
! [SV423: $i,SV86: $i,SV437: $i,SV162: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
!= ( ti @ arrow_1212486748le_alt @ SV437 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV423 ) @ SV437 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1894,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(1895,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(1896,plain,
! [SV424: $i,SV89: $i,SV438: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV424 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1897,plain,
! [SV425: $i,SV89: $i,SV439: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV439 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV439 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV425 ) @ SV439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1898,plain,
! [SV426: $i,SV89: $i,SV440: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV426 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV426 ) @ SV440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1899,plain,
! [SV427: $i,SV89: $i,SV441: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV441 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV427 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV427 ) @ SV441 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(1900,plain,
! [SV428: $i,SV89: $i,SV442: $i,SV165: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV442 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV428 ) @ SV442 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1901,plain,
! [SV429: $i,SV165: $i,SV443: $i,SV89: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV443 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV429 ) @ SV443 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(1902,plain,
! [SV469: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(1903,plain,
! [SV470: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(1904,plain,
! [SV471: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(1905,plain,
! [SV472: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV472 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(1906,plain,
! [SV473: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1907,plain,
! [SV474: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV474 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(1908,plain,
! [SV475: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV475 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(1909,plain,
! [SV476: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(1910,plain,
! [SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i,SV95: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1911,plain,
! [SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i,SV95: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(1912,plain,
! [SV267: $i] :
( ( ( ~ ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1837]) ).
thf(1913,plain,
! [SV267: $i] :
( ( ( ~ ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1837]) ).
thf(1914,plain,
! [SV267: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1915,plain,
! [SV267: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1916,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV477: $i] :
( ( ( ! [SY2207: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SY2207 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2207 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SY2207 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2207 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SY2207 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SY2207 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SY2207 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SY2207 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SY2207 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SY2207 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(1917,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV478: $i] :
( ( ( ! [SY2208: $i] :
( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SY2208 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2208 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SY2208 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2208 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SY2208 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SY2208 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SY2208 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SY2208 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SY2208 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SY2208 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(1918,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1919,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(1920,plain,
! [SV394: $i,SV217: $i,SV272: $i,SV381: $i,SV172: $i,SV103: $i] :
( ( ( ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
!= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) ) )
= $true )
| ( ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(1921,plain,
! [SV395: $i,SV382: $i,SV172: $i,SV217: $i,SV272: $i,SV103: $i] :
( ( ( ( ( ti @ SV103 @ SV272 )
!= ( ti @ SV103 @ SV217 ) ) )
= $true )
| ( ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(1922,plain,
! [SV445: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1923,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1924,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1925,plain,
! [SV446: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV446 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(1926,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(1927,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1928,plain,
! [SV447: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1929,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1930,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1931,plain,
! [SV448: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV448 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1932,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1933,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
| ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1934,plain,
! [SV449: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV449 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1935,plain,
! [SV450: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV450 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1936,plain,
! [SV451: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV451 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1937,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1938,plain,
! [SV479: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV479 ) ) @ c ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(1939,plain,
! [SV480: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV480 ) ) @ c ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1940,plain,
! [SV481: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1941,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1942,plain,
! [SV482: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV482 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(1943,plain,
! [SV483: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV483 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(1944,plain,
! [SV484: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV484 ) ) @ e ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(1945,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(1946,plain,
! [SV341: $i,SV361: $i,SV461: $i,SV452: $i,SV174: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SV461 ) ) @ SV361 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV452 ) @ SV461 ) ) @ SV341 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1947,plain,
! [SV361: $i,SV341: $i,SV462: $i,SV453: $i,SV174: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SV462 ) ) @ SV341 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ SV105 @ SV174 ) @ ( fun @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ bool ) @ ( member @ ( product_prod @ SV105 @ SV174 ) ) @ ( hAPP @ SV174 @ ( product_prod @ SV105 @ SV174 ) @ ( hAPP @ SV105 @ ( fun @ SV174 @ ( product_prod @ SV105 @ SV174 ) ) @ ( product_Pair @ SV105 @ SV174 ) @ SV453 ) @ SV462 ) ) @ SV361 ) )
= $true )
| ( ( ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV361 )
= ( ti @ ( fun @ ( product_prod @ SV105 @ SV174 ) @ bool ) @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1948,plain,
! [SV362: $i,SV342: $i,SV175: $i,SV106: $i] :
( ( ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1949,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ~ ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1950,plain,
! [SV363: $i,SV454: $i,SV410: $i,SV343: $i,SV175: $i,SV106: $i] :
( ( ( ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
!= ( hAPP @ SV106 @ SV175 @ SV343 @ SV454 ) ) )
= $true )
| ( ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SV454 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV454 ) @ SV363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(1951,plain,
! [SV455: $i,SV463: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(1952,plain,
! [SV464: $i,SV456: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(1953,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) )
| ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(1954,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
| ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1955,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) )
| ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(1956,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
| ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1957,plain,
! [SV465: $i,SV457: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SV465 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SV465 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(1958,plain,
! [SV466: $i,SV458: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV466 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(1959,plain,
! [SV467: $i,SV459: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(1960,plain,
! [SV468: $i,SV460: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(1961,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1883]) ).
thf(1962,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1884]) ).
thf(1963,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(1964,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1965,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1966,plain,
! [SV418: $i,SV86: $i,SV432: $i,SV162: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV432 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV418 ) @ SV432 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1967,plain,
! [SV419: $i,SV86: $i,SV433: $i,SV162: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV433 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV433 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV419 ) @ SV433 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1968,plain,
! [SV434: $i,SV420: $i,SV162: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV420 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV434 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV420 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(1969,plain,
! [SV435: $i,SV421: $i,SV162: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ SV421 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV435 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV421 ) @ SV435 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(1970,plain,
! [SV423: $i,SV86: $i,SV437: $i,SV162: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV437 ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
!= ( ti @ arrow_1212486748le_alt @ SV162 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV423 ) @ SV437 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1971,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1972,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1973,plain,
! [SV424: $i,SV165: $i,SV438: $i,SV89: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV424 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1974,plain,
! [SV425: $i,SV165: $i,SV439: $i,SV89: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV439 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV439 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV425 ) @ SV439 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1975,plain,
! [SV440: $i,SV426: $i,SV165: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV426 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV440 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV426 ) @ SV440 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(1976,plain,
! [SV441: $i,SV427: $i,SV165: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ SV427 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV165 )
= ( ti @ arrow_1212486748le_alt @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV427 ) @ SV441 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(1977,plain,
! [SV429: $i,SV165: $i,SV443: $i,SV89: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV443 ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
!= ( ti @ arrow_1212486748le_alt @ SV165 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV429 ) @ SV443 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1978,plain,
! [SV469: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV469 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(1979,plain,
! [SV470: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(1980,plain,
! [SV471: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(1981,plain,
! [SV472: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV472 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(1982,plain,
! [SV473: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(1983,plain,
! [SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV474 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(1984,plain,
! [SV475: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV475 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(1985,plain,
! [SV476: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(1986,plain,
! [SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(1987,plain,
! [SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1988,plain,
! [SV267: $i] :
( ( ( ! [SY2076: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2076 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2076 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1989,plain,
! [SV267: $i] :
( ( ( ! [SY2077: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SY2077 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SY2077 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1990,plain,
! [SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1991,plain,
! [SV267: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(1992,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(1993,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(1994,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(1995,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1996,plain,
! [SV394: $i,SV217: $i,SV272: $i,SV381: $i,SV172: $i,SV103: $i] :
( ( ( ( hAPP @ SV103 @ SV172 @ SV381 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV381 @ SV217 ) )
= $false )
| ( ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV381 ) @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(1997,plain,
! [SV395: $i,SV382: $i,SV172: $i,SV217: $i,SV272: $i,SV103: $i] :
( ( ( ( ti @ SV103 @ SV272 )
= ( ti @ SV103 @ SV217 ) )
= $false )
| ( ( ( hAPP @ SV103 @ SV172 @ SV382 @ SV272 )
= ( hAPP @ SV103 @ SV172 @ SV382 @ SV217 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV217 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ SV103 @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( member @ SV103 ) @ SV272 ) @ SV395 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV103 @ bool ) @ bool @ ( hAPP @ ( fun @ SV103 @ SV172 ) @ ( fun @ ( fun @ SV103 @ bool ) @ bool ) @ ( inj_on @ SV103 @ SV172 ) @ SV382 ) @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1998,plain,
! [SV445: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(1999,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(2000,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(2001,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2002,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2003,plain,
! [SV446: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV446 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2004,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1926]) ).
thf(2005,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1926]) ).
thf(2006,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(2007,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(2008,plain,
! [SV447: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV447 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2009,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2010,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2011,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2012,plain,
( ( ~ ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2013,plain,
! [SV448: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV448 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2014,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(2015,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(2016,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(2017,plain,
( ( ~ ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1933]) ).
thf(2018,plain,
! [SV449: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV449 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2019,plain,
! [SV450: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV450 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2020,plain,
! [SV451: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV451 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2021,plain,
! [SV487: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV487 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV487 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2022,plain,
! [SV479: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV479 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2023,plain,
! [SV480: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV480 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2024,plain,
! [SV481: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1940]) ).
thf(2025,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2026,plain,
! [SV482: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV482 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2027,plain,
! [SV483: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV483 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(2028,plain,
! [SV484: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV484 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2029,plain,
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2030,plain,
! [SV362: $i,SV342: $i,SV175: $i,SV106: $i] :
( ( ( ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
= ( hAPP @ SV106 @ SV175 @ SV342 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2031,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
!= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2032,plain,
! [SV363: $i,SV454: $i,SV410: $i,SV343: $i,SV175: $i,SV106: $i] :
( ( ( ( hAPP @ SV106 @ SV175 @ SV343 @ SV410 )
= ( hAPP @ SV106 @ SV175 @ SV343 @ SV454 ) )
= $false )
| ( ( ( ti @ SV106 @ SV410 )
= ( ti @ SV106 @ SV454 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV454 ) @ SV363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ SV106 @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( member @ SV106 ) @ SV410 ) @ SV363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV343 ) @ SV363 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2033,plain,
! [SV455: $i,SV463: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2034,plain,
! [SV464: $i,SV456: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2035,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1953]) ).
thf(2036,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1953]) ).
thf(2037,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(2038,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(2039,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2040,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2041,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1956]) ).
thf(2042,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1956]) ).
thf(2043,plain,
! [SV465: $i,SV457: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SV465 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SV465 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2044,plain,
! [SV466: $i,SV458: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV466 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2045,plain,
! [SV467: $i,SV459: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2046,plain,
! [SV468: $i,SV460: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2047,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2048,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2049,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2050,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2051,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1965]) ).
thf(2052,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1965]) ).
thf(2053,plain,
! [SV423: $i,SV437: $i,SV162: $i,SV86: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV86 )
= ( ti @ arrow_1212486748le_alt @ SV162 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV162 )
= ( ti @ arrow_1212486748le_alt @ SV437 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV86 ) @ SV162 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ SV423 ) @ SV437 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2054,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2055,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2056,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2057,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2058,plain,
! [SV429: $i,SV443: $i,SV165: $i,SV89: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV165 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV89 )
= ( ti @ arrow_1212486748le_alt @ SV443 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV89 ) @ SV165 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ SV429 ) @ SV443 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2059,plain,
! [SV469: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV469 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2060,plain,
! [SV470: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2061,plain,
! [SV471: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2062,plain,
! [SV472: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV472 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2063,plain,
! [SV473: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2064,plain,
! [SV474: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV474 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2065,plain,
! [SV475: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV475 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2066,plain,
! [SV476: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2067,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2068,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2069,plain,
! [SV488: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SV488 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SV488 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2070,plain,
! [SV489: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SV489 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SV489 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2071,plain,
! [SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2072,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2073,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2074,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2075,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2076,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2077,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2078,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2079,plain,
! [SV445: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV445 ) ) @ n ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2080,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2081,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2082,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2001]) ).
thf(2083,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2084,plain,
! [SV446: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV446 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2085,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2086,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2087,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2088,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2089,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2090,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2091,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2092,plain,
( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2012]) ).
thf(2093,plain,
! [SV448: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV448 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV448 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2094,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2095,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2096,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2097,plain,
( ( ! [SX0: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2098,plain,
! [SV449: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV449 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV449 ) ) @ n ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2099,plain,
! [SV450: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV450 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV450 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2100,plain,
! [SV451: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV451 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2101,plain,
! [SV487: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV487 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV487 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2102,plain,
! [SV479: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV479 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2103,plain,
! [SV480: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV480 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2104,plain,
! [SV481: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2105,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2106,plain,
! [SV482: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV482 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2107,plain,
! [SV483: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV483 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2108,plain,
! [SV484: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV484 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2109,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2110,plain,
! [SV175: $i,SV342: $i,SV362: $i,SV106: $i] :
( ( ( ( ti @ SV106 @ ( sK10_X_1 @ SV362 @ SV342 @ SV175 @ SV106 ) )
= ( ti @ SV106 @ ( sK11_SY1310 @ SV362 @ SV342 @ SV175 @ SV106 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ SV106 @ bool ) @ bool @ ( hAPP @ ( fun @ SV106 @ SV175 ) @ ( fun @ ( fun @ SV106 @ bool ) @ bool ) @ ( inj_on @ SV106 @ SV175 ) @ SV342 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2111,plain,
! [SV455: $i,SV219: $i,SV463: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2112,plain,
! [SV464: $i,SV219: $i,SV456: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2113,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1977: $i,SY1978: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1977 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1978 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1977 ) @ SY1978 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2114,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1979: $i,SY1980: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1979 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1980 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1979 ) @ SY1980 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2036]) ).
thf(2115,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2116,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2117,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1989: $i,SY1990: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1989 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1989 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1990 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1989 ) @ SY1990 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2118,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1991: $i,SY1992: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1991 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1991 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY1992 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1991 ) @ SY1992 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2119,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2120,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2121,plain,
! [SV465: $i,SV457: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SV465 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SV465 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2122,plain,
! [SV466: $i,SV458: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV466 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2123,plain,
! [SV467: $i,SV459: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2124,plain,
! [SV468: $i,SV460: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2125,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2126,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2127,plain,
! [SV108: $i,SV177: $i,SV365: $i,SV345: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2128,plain,
! [SV177: $i,SV108: $i,SV345: $i,SV365: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2129,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2130,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2131,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2132,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2133,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2134,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2135,plain,
! [SV469: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
= n )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV469 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2136,plain,
! [SV470: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 )
= n )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2137,plain,
! [SV471: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2138,plain,
! [SV472: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV472 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2139,plain,
! [SV473: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2140,plain,
! [SV474: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV474 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2141,plain,
! [SV475: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV475 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2142,plain,
! [SV476: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2143,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2144,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2145,plain,
! [SV488: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SV488 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SV488 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2069]) ).
thf(2146,plain,
! [SV489: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SV489 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SV489 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2147,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2148,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2149,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
| ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2150,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2151,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2152,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2153,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2154,plain,
! [SV490: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2155,plain,
! [SV491: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV491 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2156,plain,
! [SV492: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2157,plain,
! [SV493: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2158,plain,
! [SV446: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV446 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV446 ) ) @ n ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2159,plain,
! [SV494: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2160,plain,
! [SV495: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2161,plain,
! [SV496: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
!= n )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2162,plain,
! [SV497: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2163,plain,
! [SV498: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2164,plain,
! [SV499: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV499 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2165,plain,
! [SV500: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV500 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2166,plain,
! [SV501: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2167,plain,
! [SV502: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV502 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2168,plain,
! [SV503: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2169,plain,
! [SV504: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
!= n )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2170,plain,
! [SV505: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2171,plain,
! [SV451: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV451 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV451 ) ) @ n ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2172,plain,
! [SV487: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV487 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV487 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2173,plain,
! [SV479: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV479 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2174,plain,
! [SV480: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV480 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2175,plain,
! [SV481: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2176,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ c ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2177,plain,
! [SV482: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV482 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2178,plain,
! [SV483: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV483 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2179,plain,
! [SV484: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV484 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2180,plain,
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ! [SX0: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SX0 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SX0 ) ) @ e ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2181,plain,
! [SV455: $i,SV219: $i,SV463: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2182,plain,
! [SV464: $i,SV219: $i,SV456: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2183,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV506: $i] :
( ( ! [SY2209: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SY2209 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2209 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2209 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2209 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SY2209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2184,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV507: $i] :
( ( ! [SY2210: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SY2210 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2210 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2210 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SY2210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2185,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) )
| ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2186,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) )
| ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2187,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV508: $i] :
( ( ! [SY2211: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SY2211 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2211 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2211 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SY2211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2188,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV509: $i] :
( ( ! [SY2212: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SY2212 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SY2212 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SY2212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2189,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) )
| ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2190,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) )
| ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2191,plain,
! [SV465: $i,SV457: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SV465 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV176 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SV465 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2192,plain,
! [SV466: $i,SV458: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV466 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2193,plain,
! [SV467: $i,SV459: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2194,plain,
! [SV468: $i,SV460: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2195,plain,
! [SV177: $i,SV108: $i,SV344: $i,SV364: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2196,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2197,plain,
! [SV177: $i,SV108: $i,SV345: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2198,plain,
! [SV177: $i,SV108: $i,SV345: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2199,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2200,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2201,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2202,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2203,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2204,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2205,plain,
! [SV469: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
= n )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV469 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV469 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2206,plain,
! [SV470: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV470 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV470 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2207,plain,
! [SV471: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2208,plain,
! [SV472: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV472 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2209,plain,
! [SV473: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
= n )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2210,plain,
! [SV474: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV474 )
= n )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2211,plain,
! [SV475: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV475 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2212,plain,
! [SV476: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2213,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2214,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2215,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2144]) ).
thf(2216,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2144]) ).
thf(2217,plain,
! [SV488: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SV488 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SV488 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2218,plain,
! [SV489: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK21_SY1318 @ SV267 ) @ SV489 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( sK20_X_1 @ SV267 ) @ SV489 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2219,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK21_SY1318 @ SV267 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( sK22_SY1323 @ SV267 ) ) @ ( sK23_SY1327 @ SV267 ) ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV267 @ ( sK20_X_1 @ SV267 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2220,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2148]) ).
thf(2221,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2148]) ).
thf(2222,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2223,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2224,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2225,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2226,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2227,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2228,plain,
! [SV490: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2229,plain,
! [SV491: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV491 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2230,plain,
! [SV492: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2156]) ).
thf(2231,plain,
! [SV493: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2232,plain,
! [SV494: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2233,plain,
! [SV495: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2234,plain,
! [SV496: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2161]) ).
thf(2235,plain,
! [SV497: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2236,plain,
! [SV498: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2237,plain,
! [SV499: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV499 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2238,plain,
! [SV500: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV500 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2239,plain,
! [SV501: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2240,plain,
! [SV502: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV502 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2241,plain,
! [SV503: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2242,plain,
! [SV504: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2243,plain,
! [SV505: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2244,plain,
! [SV479: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV479 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2245,plain,
! [SV480: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV480 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2246,plain,
! [SV481: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2247,plain,
! [SV510: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV510 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2248,plain,
! [SV482: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV482 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2249,plain,
! [SV483: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV483 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2250,plain,
! [SV484: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV484 ) ) @ e ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2251,plain,
! [SV511: $i] :
( ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV511 ) ) @ n ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV511 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV511 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2252,plain,
! [SV455: $i,SV219: $i,SV463: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2253,plain,
! [SV464: $i,SV219: $i,SV456: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2254,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV512: $i,SV506: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2255,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV513: $i,SV507: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2256,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2257,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2258,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2186]) ).
thf(2259,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2186]) ).
thf(2260,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV514: $i,SV508: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2261,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV515: $i,SV509: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2262,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2263,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2189]) ).
thf(2264,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2265,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ~ ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2266,plain,
! [SV465: $i,SV457: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV457 ) @ SV465 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV457 )
= ( ti @ arrow_1212486748le_alt @ SV465 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2267,plain,
! [SV219: $i,SV176: $i,SV458: $i,SV466: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV466 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2268,plain,
! [SV219: $i,SV459: $i,SV176: $i,SV467: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2269,plain,
! [SV460: $i,SV219: $i,SV176: $i,SV468: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2270,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2195]) ).
thf(2271,plain,
! [SV177: $i,SV108: $i,SV345: $i,SV365: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2272,plain,
! [SV109: $i,SV220: $i,SV273: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2273,plain,
! [SV109: $i,SV273: $i,SV220: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2274,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2275,plain,
! [SV87: $i,SV262: $i,SV211: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2276,plain,
! [SV87: $i,SV211: $i,SV262: $i,SV163: $i,SV386: $i,SV367: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2277,plain,
! [SV163: $i,SV386: $i,SV367: $i,SV87: $i,SV262: $i,SV211: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2278,plain,
! [SV471: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV471 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV471 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2279,plain,
! [SV472: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV472 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV472 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2280,plain,
! [SV473: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
= n )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV473 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV473 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2281,plain,
! [SV474: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV474 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV474 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2282,plain,
! [SV475: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV475 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2283,plain,
! [SV476: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2284,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2285,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2214]) ).
thf(2286,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2215]) ).
thf(2287,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2288,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2289,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2290,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2291,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2292,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2293,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2294,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV379: $i,SV359: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2295,plain,
! [SV170: $i,SV359: $i,SV99: $i,SV215: $i,SV379: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2296,plain,
! [SV490: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2297,plain,
! [SV491: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV491 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2298,plain,
! [SV492: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2299,plain,
! [SV493: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2300,plain,
! [SV494: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2301,plain,
! [SV495: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2302,plain,
! [SV496: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2303,plain,
! [SV497: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2304,plain,
! [SV498: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2305,plain,
! [SV499: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV499 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2306,plain,
! [SV500: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV500 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2307,plain,
! [SV501: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2308,plain,
! [SV502: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV502 ) ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2309,plain,
! [SV503: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2310,plain,
! [SV504: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2311,plain,
! [SV505: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2312,plain,
! [SV479: $i] :
( ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV479 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2313,plain,
! [SV480: $i] :
( ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV480 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2314,plain,
! [SV481: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2246]) ).
thf(2315,plain,
! [SV510: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 )
!= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV510 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2316,plain,
! [SV482: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV482 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV482 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2317,plain,
! [SV483: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV483 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV483 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2318,plain,
! [SV484: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV484 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2319,plain,
! [SV511: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV511 ) ) @ n ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV511 )
= n )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV511 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2320,plain,
! [SV455: $i,SV219: $i,SV176: $i,SV463: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV455 ) @ SV463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV455 )
= ( ti @ arrow_1212486748le_alt @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2321,plain,
! [SV464: $i,SV107: $i,SV219: $i,SV176: $i,SV456: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2322,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV512: $i,SV506: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2323,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV513: $i,SV507: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2324,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1981: $i,SY1982: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1981 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1981 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1982 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1981 ) @ SY1982 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2256]) ).
thf(2325,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1983: $i,SY1984: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1983 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1984 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1983 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1983 ) @ SY1984 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2257]) ).
thf(2326,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1985: $i,SY1986: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1985 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1985 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1986 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1985 ) @ SY1986 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2258]) ).
thf(2327,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1987: $i,SY1988: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1987 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY1988 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1987 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1987 ) @ SY1988 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2259]) ).
thf(2328,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV514: $i,SV508: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2329,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV515: $i,SV509: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2330,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1993: $i,SY1994: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1993 )
= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1993 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1993 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1994 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1993 ) @ SY1994 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2331,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1995: $i,SY1996: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1995 )
= ( ti @ arrow_1212486748le_alt @ SY1996 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1995 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SY1995 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1995 ) @ SY1996 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2263]) ).
thf(2332,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1997: $i,SY1998: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1997 )
= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1997 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1997 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY1998 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1997 ) @ SY1998 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2264]) ).
thf(2333,plain,
! [SV176: $i,SV107: $i,SV219: $i] :
( ( ! [SY1999: $i,SY2000: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SY1999 )
= ( ti @ arrow_1212486748le_alt @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SY1999 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SY1999 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SY1999 ) @ SY2000 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2334,plain,
! [SV219: $i,SV176: $i,SV458: $i,SV466: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV458 ) @ SV176 ) ) @ SV219 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV458 ) @ SV466 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV458 )
= ( ti @ arrow_1212486748le_alt @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2335,plain,
! [SV219: $i,SV459: $i,SV107: $i,SV467: $i,SV176: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV467 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2336,plain,
! [SV460: $i,SV219: $i,SV107: $i,SV468: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV460 ) @ SV468 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV460 )
= ( ti @ arrow_1212486748le_alt @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2337,plain,
! [SV108: $i,SV177: $i,SV364: $i,SV344: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV344 ) @ SV364 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV364 ) @ SV344 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK28_I @ SV364 @ SV344 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV344 )
= ( ti @ arrow_1212486748le_alt @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2338,plain,
! [SV177: $i,SV108: $i,SV345: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV108 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV177 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV345 ) @ SV365 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV177 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV365 ) @ SV345 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV108 @ ( sK27_I @ SV365 @ SV345 @ SV177 @ SV108 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV108 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV177 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV345 )
= ( ti @ arrow_1212486748le_alt @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2339,plain,
! [SV178: $i,SV314: $i,SV346: $i,SV109: $i,SV273: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2340,plain,
! [SV109: $i,SV273: $i,SV220: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2341,plain,
! [SV163: $i,SV366: $i,SV385: $i,SV87: $i,SV262: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2342,plain,
! [SV87: $i,SV262: $i,SV211: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2343,plain,
! [SV163: $i,SV367: $i,SV386: $i,SV87: $i,SV262: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2344,plain,
! [SV163: $i,SV386: $i,SV367: $i,SV87: $i,SV262: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2345,plain,
! [SV475: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV475 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV475 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2346,plain,
! [SV476: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ c ) @ d ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2347,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2348,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2349,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2350,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2351,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2352,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2353,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2354,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2355,plain,
! [SV170: $i,SV358: $i,SV99: $i,SV215: $i,SV378: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2356,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2357,plain,
! [SV170: $i,SV359: $i,SV99: $i,SV215: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2358,plain,
! [SV170: $i,SV359: $i,SV99: $i,SV215: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2359,plain,
! [SV490: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2360,plain,
! [SV491: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 )
= n )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV491 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2361,plain,
! [SV492: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2362,plain,
! [SV493: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2363,plain,
! [SV494: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2364,plain,
! [SV495: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2365,plain,
! [SV496: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
!= n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2366,plain,
! [SV497: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2367,plain,
! [SV498: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2304]) ).
thf(2368,plain,
! [SV499: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 )
= n )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV499 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2369,plain,
! [SV500: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV500 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2370,plain,
! [SV501: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2371,plain,
! [SV502: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV502 ) ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2372,plain,
! [SV503: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 )
= n )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2373,plain,
! [SV504: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) )
| ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
!= n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2374,plain,
! [SV505: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2375,plain,
! [SV479: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV479 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV479 ) ) @ n ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2376,plain,
! [SV480: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV480 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV480 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2377,plain,
! [SV481: $i] :
( ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2378,plain,
! [SV510: $i] :
( ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV510 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2379,plain,
! [SV484: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV484 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV484 ) ) @ n ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2380,plain,
! [SV511: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV511 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV511 ) ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV511 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2381,plain,
! [SV219: $i,SV456: $i,SV176: $i,SV464: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV456 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV456 ) @ SV464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV456 )
= ( ti @ arrow_1212486748le_alt @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2382,plain,
! [SV506: $i,SV512: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2383,plain,
! [SV507: $i,SV513: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2384,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV516: $i] :
( ( ! [SY2213: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SY2213 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2213 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2213 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SY2213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2385,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV517: $i] :
( ( ! [SY2214: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SY2214 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2214 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SY2214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2386,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV518: $i] :
( ( ! [SY2215: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SY2215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2215 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2215 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SY2215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2387,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV519: $i] :
( ( ! [SY2216: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SY2216 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SY2216 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SY2216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2388,plain,
! [SV514: $i,SV508: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2389,plain,
! [SV515: $i,SV509: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2390,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV520: $i] :
( ( ! [SY2217: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SY2217 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2217 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SY2217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2391,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV521: $i] :
( ( ! [SY2218: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SY2218 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SY2218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2392,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV522: $i] :
( ( ! [SY2219: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SY2219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SY2219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SY2219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2393,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV523: $i] :
( ( ! [SY2220: $i] :
( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SY2220 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SY2220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2394,plain,
! [SV219: $i,SV459: $i,SV107: $i,SV467: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2395,plain,
! [SV109: $i,SV273: $i,SV220: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2396,plain,
! [SV87: $i,SV262: $i,SV211: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2397,plain,
! [SV163: $i,SV386: $i,SV367: $i,SV87: $i,SV262: $i,SV211: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2398,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2399,plain,
! [SV95: $i,SV266: $i,SV213: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2400,plain,
! [SV95: $i,SV213: $i,SV266: $i,SV167: $i,SV390: $i,SV374: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2401,plain,
! [SV167: $i,SV390: $i,SV374: $i,SV95: $i,SV266: $i,SV213: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2402,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV485: $i,SV477: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2403,plain,
! [SV406: $i,SV354: $i,SV268: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2404,plain,
! [SV268: $i,SV406: $i,SV354: $i,SV486: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2405,plain,
! [SV354: $i,SV406: $i,SV268: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2406,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2407,plain,
! [SV170: $i,SV359: $i,SV99: $i,SV215: $i,SV379: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2408,plain,
! [SV490: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2409,plain,
! [SV491: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV491 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2410,plain,
! [SV492: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2411,plain,
! [SV493: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2412,plain,
! [SV494: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2413,plain,
! [SV495: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2414,plain,
! [SV496: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2415,plain,
! [SV497: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2416,plain,
! [SV498: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2417,plain,
! [SV499: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV499 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2418,plain,
! [SV500: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV500 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2419,plain,
! [SV501: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2420,plain,
! [SV502: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV502 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2421,plain,
! [SV503: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 )
= n )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2422,plain,
! [SV504: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2423,plain,
! [SV505: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2374]) ).
thf(2424,plain,
! [SV481: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV481 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV481 ) ) @ n ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2425,plain,
! [SV510: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV510 ) ) @ c ) @ e ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV510 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2426,plain,
! [SV506: $i,SV512: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2427,plain,
! [SV507: $i,SV513: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2428,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV524: $i,SV516: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2429,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV525: $i,SV517: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2430,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV526: $i,SV518: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2431,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV527: $i,SV519: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2432,plain,
! [SV514: $i,SV508: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2433,plain,
! [SV515: $i,SV509: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2434,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV528: $i,SV520: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2435,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV529: $i,SV521: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2436,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV530: $i,SV522: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2437,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV531: $i,SV523: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2438,plain,
! [SV467: $i,SV176: $i,SV219: $i,SV459: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV459 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV459 ) ) @ SV219 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV459 ) @ SV467 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV459 )
= ( ti @ arrow_1212486748le_alt @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2439,plain,
! [SV109: $i,SV273: $i,SV220: $i,SV178: $i,SV346: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV178 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV109 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV314 ) @ SV346 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV178 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV220 ) @ SV273 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV109 @ ( sK33_I @ SV346 @ SV314 @ SV273 @ SV220 @ SV178 @ SV109 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV109 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV178 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV346 )
= ( ti @ arrow_1212486748le_alt @ SV220 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV220 )
= ( ti @ arrow_1212486748le_alt @ SV273 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV314 )
= ( ti @ arrow_1212486748le_alt @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2440,plain,
! [SV87: $i,SV262: $i,SV211: $i,SV163: $i,SV385: $i,SV366: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV366 ) @ SV385 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK30_I @ SV385 @ SV366 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV366 )
= ( ti @ arrow_1212486748le_alt @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2441,plain,
! [SV163: $i,SV386: $i,SV367: $i,SV87: $i,SV262: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV87 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV163 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV367 ) @ SV386 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV163 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV211 ) @ SV262 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV87 @ ( sK29_I @ SV386 @ SV367 @ SV262 @ SV211 @ SV163 @ SV87 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV87 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV163 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV211 )
= ( ti @ arrow_1212486748le_alt @ SV262 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV367 )
= ( ti @ arrow_1212486748le_alt @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2442,plain,
! [SV167: $i,SV373: $i,SV389: $i,SV95: $i,SV266: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2443,plain,
! [SV95: $i,SV266: $i,SV213: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2444,plain,
! [SV167: $i,SV374: $i,SV390: $i,SV95: $i,SV266: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2445,plain,
! [SV167: $i,SV390: $i,SV374: $i,SV95: $i,SV266: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2446,plain,
! [SV268: $i,SV354: $i,SV406: $i,SV485: $i,SV477: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2447,plain,
! [SV406: $i,SV354: $i,SV268: $i,SV485: $i,SV477: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2448,plain,
! [SV268: $i,SV354: $i,SV406: $i,SV486: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2449,plain,
! [SV354: $i,SV406: $i,SV268: $i,SV486: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2450,plain,
! [SV99: $i,SV215: $i,SV170: $i,SV378: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV358 ) @ SV378 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV378 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK32_I @ SV378 @ SV358 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV378 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV358 )
= ( ti @ arrow_1212486748le_alt @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2451,plain,
! [SV170: $i,SV359: $i,SV99: $i,SV215: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV99 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV170 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV359 ) @ SV379 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV170 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV379 ) @ SV215 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV99 @ ( sK31_I @ SV379 @ SV359 @ SV215 @ SV170 @ SV99 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV99 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV170 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV379 )
= ( ti @ arrow_1212486748le_alt @ SV215 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV359 )
= ( ti @ arrow_1212486748le_alt @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2452,plain,
! [SV490: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2453,plain,
! [SV491: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV491 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2454,plain,
! [SV492: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2455,plain,
! [SV493: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2456,plain,
! [SV494: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2457,plain,
! [SV495: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2458,plain,
! [SV496: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2459,plain,
! [SV497: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2460,plain,
! [SV498: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 ) ) @ n ) )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV498 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2461,plain,
! [SV499: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 ) ) @ n ) )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV499 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV499 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2462,plain,
! [SV500: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV500 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2463,plain,
! [SV501: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2464,plain,
! [SV502: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV502 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2465,plain,
! [SV503: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2466,plain,
! [SV504: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
!= n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2467,plain,
! [SV505: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2468,plain,
! [SV506: $i,SV219: $i,SV512: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2469,plain,
! [SV507: $i,SV219: $i,SV513: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2470,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV524: $i,SV516: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2471,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV525: $i,SV517: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2472,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV526: $i,SV518: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2473,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV527: $i,SV519: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2474,plain,
! [SV514: $i,SV219: $i,SV508: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2475,plain,
! [SV515: $i,SV219: $i,SV509: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(2476,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV528: $i,SV520: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2477,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV529: $i,SV521: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2478,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV530: $i,SV522: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2479,plain,
! [SV176: $i,SV107: $i,SV219: $i,SV531: $i,SV523: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2437]) ).
thf(2480,plain,
! [SV95: $i,SV266: $i,SV213: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2481,plain,
! [SV167: $i,SV390: $i,SV374: $i,SV95: $i,SV266: $i,SV213: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2482,plain,
! [SV406: $i,SV354: $i,SV268: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2483,plain,
! [SV354: $i,SV406: $i,SV268: $i,SV486: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2484,plain,
! [SV490: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 ) ) @ n ) )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV490 )
= n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2485,plain,
! [SV491: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 ) ) @ n ) )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV491 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV491 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2486,plain,
! [SV492: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2487,plain,
! [SV493: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(2488,plain,
! [SV494: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2489,plain,
! [SV495: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2490,plain,
! [SV496: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2491,plain,
! [SV497: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2492,plain,
! [SV500: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV500 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV500 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2493,plain,
! [SV501: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV501 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV501 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2494,plain,
! [SV502: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV502 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV502 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2495,plain,
! [SV503: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV503 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV503 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2496,plain,
! [SV504: $i] :
( ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
= n )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2497,plain,
! [SV505: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2498,plain,
! [SV506: $i,SV219: $i,SV512: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2499,plain,
! [SV507: $i,SV219: $i,SV513: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2500,plain,
! [SV516: $i,SV524: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2501,plain,
! [SV517: $i,SV525: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2502,plain,
! [SV518: $i,SV526: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2503,plain,
! [SV519: $i,SV527: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2504,plain,
! [SV514: $i,SV219: $i,SV508: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2505,plain,
! [SV515: $i,SV219: $i,SV509: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2506,plain,
! [SV528: $i,SV520: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2507,plain,
! [SV529: $i,SV521: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2508,plain,
! [SV530: $i,SV522: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2509,plain,
! [SV531: $i,SV523: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2510,plain,
! [SV95: $i,SV266: $i,SV213: $i,SV167: $i,SV389: $i,SV373: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV373 ) @ SV389 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK35_I @ SV389 @ SV373 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV389 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV373 )
= ( ti @ arrow_1212486748le_alt @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2511,plain,
! [SV167: $i,SV390: $i,SV374: $i,SV95: $i,SV266: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV95 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ f @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV374 ) @ SV390 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV167 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV213 ) @ SV266 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV95 @ ( sK34_I @ SV390 @ SV374 @ SV266 @ SV213 @ SV167 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV95 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV167 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV390 )
= ( ti @ arrow_1212486748le_alt @ SV213 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV213 )
= ( ti @ arrow_1212486748le_alt @ SV266 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV374 )
= ( ti @ arrow_1212486748le_alt @ SV390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2512,plain,
! [SV406: $i,SV354: $i,SV268: $i,SV485: $i,SV477: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV477 ) @ SV485 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK19_I @ SV485 @ SV477 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2513,plain,
! [SV354: $i,SV406: $i,SV268: $i,SV486: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV406 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV268 @ SV354 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV354 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV478 ) @ SV486 ) ) @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ SV406 @ ( sK18_I @ SV486 @ SV478 @ SV406 @ SV354 @ SV268 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV406 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool @ ( hAPP @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ SV354 ) @ arrow_1834574746e_Prof ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ bool @ arrow_612047104le_IIA @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2514,plain,
! [SV492: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV492 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV492 )
= n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2515,plain,
! [SV493: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV493 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV493 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2516,plain,
! [SV494: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV494 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
= $true )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV494 )
= n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2517,plain,
! [SV495: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV495 )
= n )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV495 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2518,plain,
! [SV496: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2490]) ).
thf(2519,plain,
! [SV497: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2520,plain,
! [SV504: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV504 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV504 )
= n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2521,plain,
! [SV505: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV505 ) ) @ n ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lba ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV505 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(2522,plain,
! [SV506: $i,SV219: $i,SV512: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2523,plain,
! [SV507: $i,SV219: $i,SV513: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2524,plain,
! [SV516: $i,SV524: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2525,plain,
! [SV517: $i,SV525: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2526,plain,
! [SV518: $i,SV526: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2527,plain,
! [SV519: $i,SV527: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2528,plain,
! [SV514: $i,SV219: $i,SV508: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2529,plain,
! [SV515: $i,SV219: $i,SV509: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2530,plain,
! [SV528: $i,SV520: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2531,plain,
! [SV529: $i,SV521: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2532,plain,
! [SV530: $i,SV522: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2533,plain,
! [SV531: $i,SV523: $i,SV176: $i,SV107: $i,SV219: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
| ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2534,plain,
! [SV496: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV496 ) ) @ c ) @ e ) ) )
= $false )
| ( ( ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV496 )
= n )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2535,plain,
! [SV497: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less @ nat ) @ ( hAPP @ arrow_1384031255e_indi @ nat @ h @ SV497 ) ) @ n ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ b ) @ a ) ) @ lab ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_992993526_mktop @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ c ) @ e ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ e ) @ d ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ arrow_844286440_mkbot @ ( hAPP @ arrow_1384031255e_indi @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ p @ SV497 ) ) @ e ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2536,plain,
! [SV506: $i,SV219: $i,SV107: $i,SV512: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV512 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2537,plain,
! [SV507: $i,SV219: $i,SV107: $i,SV513: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2538,plain,
! [SV219: $i,SV516: $i,SV524: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2539,plain,
! [SV219: $i,SV517: $i,SV525: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2540,plain,
! [SV219: $i,SV518: $i,SV526: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2541,plain,
! [SV219: $i,SV519: $i,SV527: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2542,plain,
! [SV514: $i,SV107: $i,SV219: $i,SV176: $i,SV508: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2543,plain,
! [SV515: $i,SV107: $i,SV219: $i,SV176: $i,SV509: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2544,plain,
! [SV528: $i,SV219: $i,SV520: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2545,plain,
! [SV529: $i,SV219: $i,SV521: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2546,plain,
! [SV530: $i,SV219: $i,SV522: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2547,plain,
! [SV531: $i,SV219: $i,SV523: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2548,plain,
! [SV506: $i,SV219: $i,SV107: $i,SV512: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV506 ) @ SV512 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV506 )
= ( ti @ arrow_1212486748le_alt @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2549,plain,
! [SV507: $i,SV513: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV507 ) @ SV513 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV507 )
= ( ti @ arrow_1212486748le_alt @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2550,plain,
! [SV219: $i,SV516: $i,SV524: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2551,plain,
! [SV219: $i,SV517: $i,SV525: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2552,plain,
! [SV219: $i,SV518: $i,SV526: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2553,plain,
! [SV219: $i,SV519: $i,SV527: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2554,plain,
! [SV219: $i,SV508: $i,SV107: $i,SV514: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV514 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2542]) ).
thf(2555,plain,
! [SV509: $i,SV219: $i,SV107: $i,SV515: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2556,plain,
! [SV528: $i,SV219: $i,SV520: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2557,plain,
! [SV529: $i,SV219: $i,SV521: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2558,plain,
! [SV530: $i,SV219: $i,SV522: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2559,plain,
! [SV531: $i,SV219: $i,SV523: $i,SV176: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2560,plain,
! [SV219: $i,SV516: $i,SV524: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2561,plain,
! [SV219: $i,SV517: $i,SV525: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2562,plain,
! [SV219: $i,SV518: $i,SV526: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2563,plain,
! [SV219: $i,SV519: $i,SV527: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2564,plain,
! [SV219: $i,SV508: $i,SV107: $i,SV514: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV508 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV508 ) @ SV514 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV508 )
= ( ti @ arrow_1212486748le_alt @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2565,plain,
! [SV509: $i,SV515: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV509 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV509 ) @ SV515 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV509 )
= ( ti @ arrow_1212486748le_alt @ SV515 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2566,plain,
! [SV528: $i,SV219: $i,SV520: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2567,plain,
! [SV529: $i,SV219: $i,SV521: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2568,plain,
! [SV530: $i,SV219: $i,SV522: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2569,plain,
! [SV531: $i,SV219: $i,SV523: $i,SV176: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2570,plain,
! [SV219: $i,SV524: $i,SV176: $i,SV516: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV516 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2571,plain,
! [SV525: $i,SV219: $i,SV176: $i,SV517: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV517 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2572,plain,
! [SV526: $i,SV176: $i,SV219: $i,SV518: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2573,plain,
! [SV527: $i,SV176: $i,SV219: $i,SV519: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2574,plain,
! [SV528: $i,SV107: $i,SV219: $i,SV176: $i,SV520: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2575,plain,
! [SV529: $i,SV107: $i,SV219: $i,SV176: $i,SV521: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2576,plain,
! [SV530: $i,SV107: $i,SV219: $i,SV176: $i,SV522: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
| ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2577,plain,
! [SV531: $i,SV107: $i,SV219: $i,SV176: $i,SV523: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
| ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2578,plain,
! [SV219: $i,SV524: $i,SV176: $i,SV516: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV516 ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV524 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2579,plain,
! [SV525: $i,SV219: $i,SV176: $i,SV517: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV517 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2580,plain,
! [SV526: $i,SV176: $i,SV219: $i,SV518: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV526 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2581,plain,
! [SV527: $i,SV176: $i,SV219: $i,SV519: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2582,plain,
! [SV219: $i,SV528: $i,SV176: $i,SV520: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV520 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2583,plain,
! [SV529: $i,SV219: $i,SV176: $i,SV521: $i,SV107: $i] :
( ( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
!= ( ti @ arrow_1212486748le_alt @ SV521 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2575]) ).
thf(2584,plain,
! [SV530: $i,SV176: $i,SV219: $i,SV522: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2585,plain,
! [SV531: $i,SV176: $i,SV219: $i,SV523: $i,SV107: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2586,plain,
! [SV219: $i,SV516: $i,SV107: $i,SV524: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV516 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV516 ) @ SV524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV516 )
= ( ti @ arrow_1212486748le_alt @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2587,plain,
! [SV525: $i,SV517: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV517 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV517 ) @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV517 )
= ( ti @ arrow_1212486748le_alt @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2588,plain,
! [SV219: $i,SV518: $i,SV107: $i,SV526: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV518 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV518 ) @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV518 )
= ( ti @ arrow_1212486748le_alt @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(2589,plain,
! [SV527: $i,SV519: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV519 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV519 ) @ SV527 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV519 )
= ( ti @ arrow_1212486748le_alt @ SV527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2590,plain,
! [SV219: $i,SV528: $i,SV176: $i,SV520: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV520 ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV528 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2591,plain,
! [SV529: $i,SV219: $i,SV176: $i,SV521: $i,SV107: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV521 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2592,plain,
! [SV530: $i,SV176: $i,SV219: $i,SV522: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
= $false )
| ( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
!= ( ti @ arrow_1212486748le_alt @ SV530 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2593,plain,
! [SV531: $i,SV176: $i,SV219: $i,SV523: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) ) )
= $true )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2594,plain,
! [SV219: $i,SV520: $i,SV107: $i,SV528: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV520 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV520 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV520 ) @ SV528 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV520 )
= ( ti @ arrow_1212486748le_alt @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2595,plain,
! [SV529: $i,SV521: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV521 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV521 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV521 ) @ SV529 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV521 )
= ( ti @ arrow_1212486748le_alt @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2596,plain,
! [SV219: $i,SV522: $i,SV107: $i,SV530: $i,SV176: $i] :
( ( ( ( ti @ arrow_1212486748le_alt @ SV176 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV522 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV522 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV522 ) @ SV530 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV522 )
= ( ti @ arrow_1212486748le_alt @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2597,plain,
! [SV531: $i,SV523: $i,SV219: $i,SV176: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV523 ) ) @ SV219 ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV107 )
= ( ti @ arrow_1212486748le_alt @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV523 ) @ SV176 ) ) @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool @ ( hAPP @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) ) @ ( product_Pair @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ SV107 ) @ SV176 ) ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( hAPP @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ arrow_1212486748le_alt @ ( fun @ arrow_1212486748le_alt @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) ) @ arrow_1726925404_above @ SV219 ) @ SV523 ) @ SV531 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_1212486748le_alt @ arrow_1212486748le_alt ) @ bool ) ) @ SV219 ) @ arrow_638930832le_Lin ) )
= $false )
| ( ( ( ti @ arrow_1212486748le_alt @ SV523 )
= ( ti @ arrow_1212486748le_alt @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2598,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[253,2597,2596,2595,2594,2589,2588,2587,2586,2565,2564,2549,2548,2535,2534,2521,2520,2517,2516,2515,2514,2513,2512,2511,2510,2495,2494,2493,2492,2485,2484,2461,2460,2451,2450,2449,2447,2445,2443,2441,2440,2439,2438,2425,2424,2381,2380,2379,2376,2375,2358,2356,2346,2345,2344,2342,2340,2338,2337,2336,2334,2320,2317,2316,2281,2280,2279,2278,2266,2219,2218,2217,2206,2205,2198,2196,2172,2171,2158,2110,2099,2098,2093,2079,2072,2058,2053,2032,2030,2008,1997,1996,1976,1975,1974,1973,1969,1968,1967,1966,1947,1946,1900,1892,1834,1833,1795,1792,1765,1764,1761,1760,1752,1751,1745,1740,1739,1724,1723,1685,1666,1665,1662,1653,1629,1604,1603,1595,1594,1584,1583,1582,1561,1547,1513,1505,1485,1484,1471,1470,1443,1438,1428,1416,1415,1411,1392,1391,1390,1386,1385,1384,1383,1382,1381,1380,1377,1352,1306,1302,1301,1271,1264,1263,1253,1249,1237,1235,1214,1213,1206,1205,1204,1203,1202,1200,1199,1192,1175,1115,1114,1098,1066,1065,1064,1063,1035,1034,1033,1029,1028,1020,1019,999,972,971,952,951,938,937,918,899,898,845,842,841,840,839,834,833,799,798,797,747,746,741,737,697,696,695,694,693,692,649,646,643,640,634,626,621,591,590,589,584,581,580,579,577,542,525,524,523,518,499,473,472,468,467,462,460,455,416,406,405,404,403,402,401,400,399,392,391,383,367,366,365,315,314,313,312,311,308,307,298,296,295,294,293,292,291,290,289,288,282,281,270,264,263,262,261,260,259,258,257,256,255,254]) ).
thf(2599,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2598]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SCT171+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 01:41:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.41/0.59 ...
% 3.43/3.61
% 3.43/3.61 No.of.Axioms: 168
% 3.43/3.61
% 3.43/3.61 Length.of.Defs: 0
% 3.43/3.61
% 3.43/3.61 Contains.Choice.Funs: false
% 3.56/3.71 ............
% 5.90/6.14 (rf:2,axioms:152,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:170,loop_count:0,foatp_calls:0,translation:fof_full)..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 78.20/78.39 .........................................ignored arguments false
% 78.48/78.74 ....
% 81.15/81.32 (rf:0,axioms:168,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:170,loop_count:0,foatp_calls:0,translation:fof_full)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
% 117.24/117.43
% 117.24/117.43 ********************************
% 117.24/117.43 * All subproblems solved! *
% 117.24/117.43 ********************************
% 117.24/117.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:168,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:38,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2598,loop_count:0,foatp_calls:1,translation:fof_full)
% 135.70/135.88
% 135.70/135.88 %**** Beginning of derivation protocol ****
% 135.70/135.88 % SZS output start CNFRefutation
% See solution above
% 135.74/135.92
% 135.74/135.92 %**** End of derivation protocol ****
% 135.74/135.92 %**** no. of clauses in derivation: 2599 ****
% 135.74/135.92 %**** clause counter: 2598 ****
% 135.74/135.92
% 135.74/135.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:168,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:38,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2598,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------